Details

sample83.0ms

Algorithm

intervals

Results

38.0ms	256×	body	80	valid
22.0ms	252×	body	80	nan

simplify67.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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)
16.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
6.0ms	(* (log base) (atan2 im re))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series596.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(hypot im re)
190.0ms	(/ (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
40.0ms	(* (log base) (atan2 im re))
294.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	1150
1	307
0	137

prune666.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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:

4.0ms

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

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

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

simplify1.0s

Counts

36 → 36

Iterations

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

prune279.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

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:

9.0ms	(/ 1 (log base))
25.0ms	(* (atan2 im re) (/ 1 (log base)))

series294.0ms

Counts

2 → 6

Calls

2 calls:

234.0ms	(/ 1 (log base))
59.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify3.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	2191
1	225
0	104

prune439.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma (log base) (log base) (* 0.0 0.0)))
0.3b	(* (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (/ 1 (fma (log base) (log base) (* 0.0 0.0))))
0.3b	(* (log base) (atan2 im re))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-r`
13×	`add-cbrt-cube`
10×	`pow1`
7×	`associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `cbrt-unprod` `associate-/l`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `associate-*r/` `log-pow` `un-div-inv` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 106

Calls

4 calls:

4.0ms	(/ 1 (fma (log base) (log base) (* 0.0 0.0)))
28.0ms	(* (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (/ 1 (fma (log base) (log base) (* 0.0 0.0))))
10.0ms	(* (log base) (atan2 im re))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

435.0ms	(/ 1 (fma (log base) (log base) (* 0.0 0.0)))
235.0ms	(* (- (* (log base) (atan2 im re)) (* (log (hypot im re)) 0.0)) (/ 1 (fma (log base) (log base) (* 0.0 0.0))))
46.0ms	(* (log base) (atan2 im re))
336.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.0s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	2106
1	398
0	172

prune855.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes623.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	6
0	6

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.3s	7931×	body	80	nan