Details

sample93.0ms

Algorithm

intervals

Results

34.0ms	256×	body	80	valid
32.0ms	232×	body	80	nan

simplify141.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	100	22
6	104	22
done	104	22

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

0.0ms	(hypot re im)
18.0ms	(* (atan2 im re) (log base))
33.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series613.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(hypot re im)
49.0ms	(* (atan2 im re) (log base))
90.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
387.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.4s

Counts

91 → 91

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	153	1628
1	308	1592
2	926	1401
3	3228	1342
done	5000	1341

prune665.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 65

Calls

1 calls:

8.0ms

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

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

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

simplify4.5s

Counts

68 → 68

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	108	903
1	186	857
2	396	831
3	777	823
4	1638	823
done	5000	820

prune183.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
43×	`times-frac`
40×	`*-un-lft-identity`
38×	`add-cube-cbrt`
34×	`add-exp-log`
22×	`add-cbrt-cube`
17×	`associate-r`
16×	`associate-l`
11×	`div-exp`
10×	`pow1`
9×	`prod-exp`
7×	`unswap-sqr`
6×	`cbrt-undiv` `log-prod` `associate-/r` `associate-/l`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/`
1×	`frac-times` `flip3--` `pow-flip` `div-sub` `associate-r/` `associate-l/` `log-pow` `flip--` `inv-pow`

Counts

4 → 150

Calls

4 calls:

10.0ms	(/ 1 (hypot (log base) 0.0))
71.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0)))
9.0ms	(* (atan2 im re) (log base))
23.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0))

series923.0ms

Counts

4 → 12

Calls

4 calls:

530.0ms	(/ 1 (hypot (log base) 0.0))
247.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0)))
34.0ms	(* (atan2 im re) (log base))
111.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (hypot (log base) 0.0))

simplify1.9s

Counts

162 → 162

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	227	3597
1	533	3395
2	1707	2995
done	5000	2973

prune648.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
62×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`associate-/r/`
10×	`pow1`
8×	`div-exp`
6×	`log-prod` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `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` `frac-2neg` `1-exp` `clear-num` `log-pow`
1×	`pow-to-exp` `pow-flip` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unpow2` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 165

Calls

4 calls:

25.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im))))))
13.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))))
9.0ms	(* (atan2 im re) (log base))
3.0ms	(pow (log base) 2)

series683.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im))))))
190.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))))
35.0ms	(* (atan2 im re) (log base))
231.0ms	(pow (log base) 2)

simplify1.4s

Counts

177 → 177

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	278	5040
1	587	4725
2	1498	4251
done	5000	4196

prune669.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes235.0ms

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 (0.0ms)

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

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8016×	body	80	nan