Details

sample95.0ms

Algorithm

intervals

Results

46.0ms	256×	body	80	valid
26.0ms	254×	body	80	nan

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	18	724
1	31	594
2	52	594
3	68	594
4	88	594
5	102	594
6	106	594
done	106	594

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

3 → 69

Calls

3 calls:

27.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
7.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series552.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
51.0ms	(* (atan2 im re) (log base))
409.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.5s

Counts

78 → 78

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	141	41517
1	312	40190
2	1287	38841
done	5000	38526

prune681.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

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

simplify1.2s

Counts

36 → 36

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	64	14350
1	110	13912
2	302	13832
3	1366	13722
done	5001	13681

prune254.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
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 → 65

Calls

1 calls:

11.0ms

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

series64.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

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

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: 3 (941.0ms)

Iter	Nodes	Cost
0	108	33027
1	201	31865
2	697	31785
3	3854	31675
done	5001	31675

prune394.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (sqrt (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))
0.6b	(fma (log base) (log base) (* 0.0 0.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
12×	`sqrt-prod`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`log-prod` `associate-/r*`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate-/l*`
2×	`fma-udef` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

38.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
11.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series813.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
34.0ms	(* (atan2 im re) (log base))
345.0ms	(fma (log base) (log base) (* 0.0 0.0))
325.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.5s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	157	59660
1	340	57114
2	1405	52340
done	5000	52070

prune696.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes525.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	333
1	10	333
done	10	333

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.5s	7946×	body	80	nan