Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
16.0ms	224×	body	80	nan

simplify62.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b

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

0.4b

(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))

0.5b

(fma (log base) (log base) (* 0.0 0.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

2.0ms

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

0.0ms

(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))

0.0ms

(fma (log base) (log base) (* 0.0 0.0))

series384.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms

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

38.0ms

(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))

274.0ms

(fma (log base) (log base) (* 0.0 0.0))

simplify1.1s

Counts

58 → 58

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	93	1372
1	169	1357
2	392	1181
3	1167	1128
done	5000	1123

prune438.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:

4.0ms

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

series48.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify4.8s

Counts

68 → 68

Iterations

Useful iterations: 5 (3.5s)

Iter	Nodes	Cost
0	108	903
1	186	861
2	389	835
3	941	829
4	1924	827
5	4381	824
done	5000	824

prune176.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.4b	(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.5b	(pow (log base) 2)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
9×	`pow1`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `un-div-inv` `-commutative` `fma-udef` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

2.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
8.0ms	(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
2.0ms	(pow (log base) 2)

series474.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
72.0ms	(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
32.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
150.0ms	(pow (log base) 2)

simplify1.9s

Counts

114 → 114

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	157	2015
1	328	1874
2	829	1568
3	2886	1553
done	5000	1547

prune367.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ (/ 1 (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (pow (log base) 2)))))
0.4b	(/ (/ 1 (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.5b	(pow (log base) 2)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

283×	`times-frac`
175×	`add-sqr-sqrt`
155×	`*-un-lft-identity`
153×	`add-cube-cbrt`
84×	`sqrt-prod`
82×	`associate-r`
29×	`add-exp-log`
18×	`add-cbrt-cube`
15×	`div-inv`
13×	`associate-/l*`
12×	`div-exp`
8×	`pow1`
7×	`unswap-sqr`
6×	`cbrt-undiv` `associate-/r*`
5×	`prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `cbrt-unprod`
2×	`rec-exp` `1-exp`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `-commutative` `fma-udef` `associate-/l/` `unpow2` `sqr-pow`

Counts

4 → 259

Calls

4 calls:

30.0ms	(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ (/ 1 (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (pow (log base) 2)))))
7.0ms	(/ (/ 1 (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (pow (log base) 2))))
0.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
2.0ms	(pow (log base) 2)

series964.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ (/ 1 (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (pow (log base) 2)))))
624.0ms	(/ (/ 1 (hypot 0.0 (log base))) (sqrt (fma 0.0 0.0 (pow (log base) 2))))
33.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
152.0ms	(pow (log base) 2)

simplify2.1s

Counts

271 → 271

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	350	7985
1	832	7264
2	2224	5589
done	5000	5573

prune849.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes429.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	25	23
2	27	23
done	27	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

590.0ms	7961×	body	80	nan
574.0ms	8000×	body	80	valid