Details

sample55.0ms

Algorithm

intervals

Results

18.0ms	260×	body	80	nan
18.0ms	256×	body	80	valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b

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

0.3b

(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))

0.5b

(fma (log base) (log base) (* 0.0 0.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

2.0ms

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

0.0ms

(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))

0.0ms

(fma (log base) (log base) (* 0.0 0.0))

series377.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms

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

37.0ms

(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))

272.0ms

(fma (log base) (log base) (* 0.0 0.0))

simplify935.0ms

Counts

58 → 58

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	93	1372
1	169	1357
2	392	1181
3	1170	1124
done	5001	1124

prune290.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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:

4.0ms

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

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

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

simplify2.6s

Counts

68 → 68

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	108	903
1	186	857
2	389	831
3	941	823
4	2013	823
done	5000	820

prune173.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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:

2.0ms	(/ -1 (log base))
8.0ms	(* (atan2 im re) (/ -1 (log base)))

series205.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(/ -1 (log base))
45.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify2.3s

Counts

76 → 76

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	103	741
1	208	670
2	651	612
3	2373	604
done	5000	604

prune204.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

332×	`times-frac`
165×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
63×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
54×	`pow1` `associate-/r*`
51×	`log-pow`
21×	`neg-mul-1`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 270

Calls

2 calls:

12.0ms	(/ 1 (/ (log base) (- (atan2 im re))))
5.0ms	(/ (log base) (- (atan2 im re)))

series110.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ 1 (/ (log base) (- (atan2 im re))))
53.0ms	(/ (log base) (- (atan2 im re)))

simplify2.1s

Counts

276 → 276

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	306	4755
1	651	3983
2	1196	3580
3	3063	3490
done	5000	3488

prune338.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0b

regimes210.0ms

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	8	8
1	10	8
done	10	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

572.0ms	8174×	body	80	nan
562.0ms	8000×	body	80	valid