Details

sample116.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	valid
32.0ms	228×	body	80	nan

simplify71.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	106
6	106
5	102
4	88
3	68
2	52
1	31
0	18

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot im re)
0.3b	(* (log base) (atan2 im re))
0.3b	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `hypot-udef` `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

4 → 73

Calls

4 calls:

0.0ms	(hypot im re)
9.0ms	(* (log base) (atan2 im re))
15.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series697.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot im re)
48.0ms	(* (log base) (atan2 im re))
153.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
431.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	1145
1	307
0	137

prune679.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

6.0ms

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

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

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

simplify1.1s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	1366
2	302
1	110
0	64

prune242.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (/ (log base) (atan2 im re)))
0.3b	(/ (log base) (atan2 im re))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`pow1` `associate-/r*`
16×	`log-pow`
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` `clear-num` `frac-2neg` `1-exp` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

2 → 123

Calls

2 calls:

9.0ms	(/ 1 (/ (log base) (atan2 im re)))
6.0ms	(/ (log base) (atan2 im re))

series115.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ 1 (/ (log base) (atan2 im re)))
44.0ms	(/ (log base) (atan2 im re))

simplify2.4s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	2349
1	389
0	166

prune498.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-l`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*` `div-exp` `prod-exp`
3×	`associate-r` `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-l/` `-commutative` `pow-flip` `inv-pow`

Counts

2 → 77

Calls

2 calls:

4.0ms	(/ 1 (log base))
17.0ms	(* (/ 1 (log base)) (atan2 im re))

series265.0ms

Counts

2 → 6

Calls

2 calls:

211.0ms	(/ 1 (log base))
54.0ms	(* (/ 1 (log base)) (atan2 im re))

simplify970.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1302
1	226
0	105

prune315.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes443.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	7699×	body	80	nan
1.2s	8000×	body	80	valid