Details

sample90.0ms

Algorithm

intervals

Results

30.0ms	289×	body	80	nan
27.0ms	256×	body	80	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

localize30.0ms

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))

rewrite38.0ms

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)
23.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
9.0ms	(* (atan2 im re) (log base))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series601.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(hypot re im)
128.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
48.0ms	(* (atan2 im re) (log base))
343.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

91 → 91

Iterations

Useful iterations: done (2.5s)

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

prune622.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

10.0ms

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

series48.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

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

simplify2.5s

Counts

36 → 36

Iterations

Useful iterations: 4 (309.0ms)

Iter	Nodes	Cost
0	64	394
1	105	375
2	207	351
3	385	348
4	680	344
5	2117	344
done	5000	344

prune120.0ms

Pruning

12 alts after pruning (11 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)))

rewrite26.0ms

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` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 78

Calls

2 calls:

6.0ms	(/ 1 (log base))
17.0ms	(* (atan2 im re) (/ 1 (log base)))

series274.0ms

Counts

2 → 6

Calls

2 calls:

221.0ms	(/ 1 (log base))
53.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify3.8s

Counts

84 → 84

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	104	789
1	201	614
2	435	546
3	852	540
4	1628	534
done	5000	534

prune275.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (log base) (fma 0.0 0.0 (pow (log base) 2))) (atan2 im re))
0.4b	(/ (log base) (fma 0.0 0.0 (pow (log base) 2)))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`times-frac`
17×	`pow1`
16×	`associate-l`
13×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`log-pow`
8×	`unpow-prod-down`
6×	`pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `div-exp` `pow-exp` `prod-exp` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 112

Calls

4 calls:

34.0ms	(* (/ (log base) (fma 0.0 0.0 (pow (log base) 2))) (atan2 im re))
19.0ms	(/ (log base) (fma 0.0 0.0 (pow (log base) 2)))
6.0ms	(pow (log base) 2)
5.0ms	(pow (log base) 2)

series1.2s

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (/ (log base) (fma 0.0 0.0 (pow (log base) 2))) (atan2 im re))
520.0ms	(/ (log base) (fma 0.0 0.0 (pow (log base) 2)))
205.0ms	(pow (log base) 2)
235.0ms	(pow (log base) 2)

simplify3.3s

Counts

124 → 124

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	141	1648
1	302	1573
2	810	1355
3	3561	1335
done	5001	1333

prune673.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes389.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
done	6	6

end0.0ms

sample2.6s

Algorithm

intervals

Results

882.0ms	8043×	body	80	nan
867.0ms	8000×	body	80	valid