Details

sample107.0ms

Algorithm

intervals

Results

37.0ms	255×	body	80	nan
34.0ms	256×	body	80	valid

simplify70.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (atan2 im re) (log base))
10.0ms	(* (log base) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
33.0ms	(* (atan2 im re) (log base))
167.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify755.0ms

Counts: 120 → 120

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 31

Calls

1 calls:

5.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify707.0ms

Counts: 34 → 34

prune113.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 74

Calls

2 calls:

6.0ms	(/ 1 (log base))
21.0ms	(* (atan2 im re) (/ 1 (log base)))

series280.0ms

Counts

2 → 6

Calls

2 calls:

240.0ms	(/ 1 (log base))
40.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify721.0ms

Counts: 80 → 80

prune186.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (log base) (atan2 im re))
0.7b	(/ 1 (/ (log base) (atan2 im re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 119

Calls

2 calls:

7.0ms	(/ (log base) (atan2 im re))
11.0ms	(/ 1 (/ (log base) (atan2 im re)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (log base) (atan2 im re))
68.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify600.0ms

Counts: 125 → 125

prune294.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

regimes246.0ms

Accuracy

20.4% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.5s

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	8127×	body	80	nan
1.2s	8000×	body	80	valid