Details

sample57.0ms

Algorithm

intervals

Results

18.0ms	250×	body	80	nan
17.0ms	256×	body	80	valid

simplify81.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 3 expressions with local error:

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))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

3 → 69

Calls

3 calls:

21.0ms	(/ (- (* (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))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series366.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (fma (log base) (log base) (* 0.0 0.0)))
29.0ms	(* (atan2 im re) (log base))
267.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.6s

Counts

78 → 78

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	141	1568
1	291	1534
2	900	1349
3	3204	1290
done	5000	1289

prune344.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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:

9.0ms

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

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

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

simplify1.9s

Counts

36 → 36

Iterations

Useful iterations: 4 (253.0ms)

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

prune118.0ms

Pruning

16 alts after pruning (15 fresh and 1 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)))

rewrite24.0ms

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:

5.0ms	(/ 1 (log base))
16.0ms	(* (atan2 im re) (/ 1 (log base)))

series191.0ms

Counts

2 → 6

Calls

2 calls:

152.0ms	(/ 1 (log base))
39.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: 4 (829.0ms)

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

prune168.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`add-exp-log` `times-frac`
17×	`associate-r`
13×	`add-cbrt-cube`
12×	`pow1`
6×	`log-prod` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `flip--` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

5.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
11.0ms	(* (atan2 im re) (log base))
32.0ms	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
3.0ms	(pow (log base) 2)

series452.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
27.0ms	(* (atan2 im re) (log base))
63.0ms	(* (- (* (atan2 im re) (log base)) (* 0.0 (log (hypot re im)))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
150.0ms	(pow (log base) 2)

simplify1.0s

Counts

135 → 135

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	207	2291
1	439	2080
2	1294	1804
done	5000	1790

prune396.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

regimes257.0ms

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

sample1.6s

Algorithm

intervals

Results

560.0ms	8023×	body	80	nan
552.0ms	8000×	body	80	valid