Details

sample103.0ms

Algorithm

intervals

Results

33.0ms	256×	body	80	valid
33.0ms	250×	body	80	nan

simplify88.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

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

series794.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(hypot im re)
185.0ms	(/ (fma (- 0.0) (log (hypot im re)) (* (log base) (atan2 im re))) (fma (log base) (log base) (* 0.0 0.0)))
66.0ms	(* (log base) (atan2 im re))
476.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify470.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	744
1	239
0	128

prune674.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
83×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
73×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
24×	`neg-mul-1`
23×	`pow1`
22×	`log-pow`
12×	`associate-/r*`
10×	`associate-/l*`
3×	`add-cbrt-cube` `add-exp-log`
1×	`neg-sub0` `expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `distribute-frac-neg` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 158

Calls

1 calls:

20.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify691.0ms

Counts

161 → 161

Iterations

Iter	Nodes
done	5000
2	1551
1	451
0	209

prune708.0ms

Pruning

13 alts after pruning (12 fresh and 1 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))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
59×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
52×	`add-cube-cbrt`
40×	`associate-r`
31×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
19×	`pow1`
15×	`add-exp-log`
14×	`log-pow`
12×	`associate-/r*`
10×	`associate-l`
9×	`add-cbrt-cube`
8×	`neg-mul-1`
4×	`div-exp` `prod-exp`
3×	`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×	`distribute-lft-neg-out` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

2 → 142

Calls

2 calls:

11.0ms	(/ 1 (- (log base)))
33.0ms	(* (- (atan2 im re)) (/ 1 (- (log base))))

series737.0ms

Counts

2 → 6

Calls

2 calls:

682.0ms	(/ 1 (- (log base)))
55.0ms	(* (- (atan2 im re)) (/ 1 (- (log base))))

simplify3.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
2	2550
1	467
0	169

prune571.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log (hypot im re)) (- 0.0) (* (atan2 im re) (log base)))))
0.3b	(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log (hypot im re)) (- 0.0) (* (atan2 im re) (log base))))
0.3b	(* (atan2 im re) (log base))
0.5b	(pow (log base) 2)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-exp-log`
16×	`associate-/r*`
13×	`add-cbrt-cube`
10×	`pow1`
8×	`div-exp`
6×	`log-prod` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `unpow-prod-down` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-l`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `log-pow`
1×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `pow-flip` `unpow2` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 155

Calls

4 calls:

10.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log (hypot im re)) (- 0.0) (* (atan2 im re) (log base)))))
4.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log (hypot im re)) (- 0.0) (* (atan2 im re) (log base))))
7.0ms	(* (atan2 im re) (log base))
2.0ms	(pow (log base) 2)

series859.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log (hypot im re)) (- 0.0) (* (atan2 im re) (log base)))))
259.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (fma (log (hypot im re)) (- 0.0) (* (atan2 im re) (log base))))
56.0ms	(* (atan2 im re) (log base))
251.0ms	(pow (log base) 2)

simplify1.3s

Counts

167 → 167

Iterations

Iter	Nodes
done	5001
2	2953
1	634
0	257

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes514.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	23
3	23
2	19
1	15
0	10

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.9s	7964×	body	80	nan
1.4s	8000×	body	80	valid