Details

sample53.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
16.0ms	241×	body	80	nan

simplify81.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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)
21.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
8.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series397.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
67.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
28.0ms	(* (atan2 im re) (log base))
257.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.6s

Counts

91 → 91

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	153	1628
1	308	1592
2	923	1401
3	3207	1342
done	5002	1341

prune336.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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)))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify2.8s

Counts

68 → 68

Iterations

Useful iterations: done (2.8s)

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

prune167.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 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)

rewrite53.0ms

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:

20.0ms	(/ 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)))))
11.0ms	(* (atan2 im re) (log base))
3.0ms	(pow (log base) 2)

series436.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im))))))
129.0ms	(/ (fma 0.0 0.0 (pow (log base) 2)) (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))))
27.0ms	(* (atan2 im re) (log base))
148.0ms	(pow (log base) 2)

simplify1.1s

Counts

177 → 177

Iterations

Useful iterations: done (1.1s)

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

prune493.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (+ (* (atan2 im re) (* 2 (log (cbrt base)))) (* (atan2 im re) (log (cbrt 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))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

4 → 68

Calls

4 calls:

227.0ms	(/ (- (+ (* (atan2 im re) (* 2 (log (cbrt base)))) (* (atan2 im re) (log (cbrt base)))) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series794.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (+ (* (atan2 im re) (* 2 (log (cbrt base)))) (* (atan2 im re) (log (cbrt base)))) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
263.0ms	(fma (log base) (log base) (* 0.0 0.0))
178.0ms	(cbrt base)
198.0ms	(cbrt base)

simplify714.0ms

Counts

80 → 80

Iterations

Useful iterations: done (711.0ms)

Iter	Nodes	Cost
0	131	1964
1	299	1744
2	1008	1508
done	5000	1400

prune405.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.6s

Algorithm

intervals

Results

549.0ms	8038×	body	80	nan
530.0ms	8000×	body	80	valid