Details

sample96.0ms

Algorithm

intervals

Results

35.0ms	277×	body	80	nan
31.0ms	256×	body	80	valid

simplify161.0ms

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	100	22
6	104	22
done	104	22

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 3 expressions with local error:

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))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `log-prod`
4×	`associate-r`
3×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`associate-/l/`
1×	`cbrt-undiv` `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

3 → 69

Calls

3 calls:

35.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
9.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series573.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
40.0ms	(* (atan2 im re) (log base))
428.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

78 → 78

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	141	1568
1	291	1534
2	900	1349
3	3204	1290
done	5000	1289

prune511.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

9.0ms

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

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

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

simplify4.5s

Counts

68 → 68

Iterations

Useful iterations: done (4.5s)

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

prune290.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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:

6.0ms	(/ -1 (log base))
20.0ms	(* (atan2 im re) (/ -1 (log base)))

series305.0ms

Counts

2 → 6

Calls

2 calls:

239.0ms	(/ -1 (log base))
66.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify5.0s

Counts

76 → 76

Iterations

Useful iterations: done (5.0s)

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

prune275.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
156×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
43×	`associate-/r*`
35×	`pow1`
32×	`log-pow`
16×	`neg-mul-1`
15×	`add-exp-log` `associate-/l*`
9×	`add-cbrt-cube`
8×	`div-exp`
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×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 253

Calls

2 calls:

18.0ms	(/ (- (log base)) (atan2 im re))
29.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

series182.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- (log base)) (atan2 im re))
101.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

simplify3.0s

Counts

259 → 259

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	307	4460
1	657	3767
2	1259	3396
3	3548	3309
done	5001	3308

prune583.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes239.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

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

sample4.1s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
1.2s	8045×	body	80	nan