Details

sample54.0ms

Algorithm

intervals

Results

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

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	16
done	33	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.6b	(* (log base) (log base))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `associate-l` `log-pow` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `hypot-def` `div-inv`

Counts

4 → 119

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
38.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
103.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
147.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	467	1408
1	1820	1268
2	5001	1217
done	5001	1217

prune470.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.4b	(* (log (hypot re im)) (log base))
0.4b	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.6b	(* (log base) (log base))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`pow1`
12×	`log-prod`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-r` `associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`flip3-+` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

3 → 99

Calls

3 calls:

10.0ms	(* (log (hypot re im)) (log base))
34.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
13.0ms	(* (log base) (log base))

series359.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(* (log (hypot re im)) (log base))
111.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
146.0ms	(* (log base) (log base))

simplify54.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	377	1035
1	1559	925
2	5002	895
done	5002	895

prune346.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
157×	`times-frac`
104×	`add-sqr-sqrt`
93×	`div-exp`
90×	`*-un-lft-identity`
85×	`add-cube-cbrt`
62×	`prod-exp`
50×	`add-cbrt-cube`
44×	`associate-l`
41×	`1-exp`
20×	`cbrt-undiv`
15×	`rec-exp`
14×	`associate-/r*`
13×	`cbrt-unprod`
11×	`div-inv`
7×	`pow1` `associate-r` `unswap-sqr`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 236

Calls

4 calls:

11.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
8.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
52.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))

series974.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
157.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
115.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
354.0ms	(* (/ 1 (/ (hypot (log base) 0.0) 1)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1)))

simplify92.0ms

Counts

248 → 248

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	940	3378
1	4369	2753
2	5001	2552
done	5001	2552

prune649.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
0.4b	(* (log (hypot re im)) (log base))
0.4b	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
0.6b	(pow (log base) 2)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

151×	`times-frac`
109×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
88×	`add-cube-cbrt`
48×	`add-exp-log` `associate-r`
24×	`div-exp`
20×	`add-cbrt-cube`
13×	`pow1` `associate-/r*`
12×	`1-exp`
11×	`prod-exp`
9×	`div-inv`
8×	`unswap-sqr`
7×	`associate-l`
6×	`cbrt-undiv` `rec-exp` `log-prod`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `log-pow` `associate-/l*`
2×	`frac-times` `flip3-+` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `flip-+`
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 → 214

Calls

4 calls:

11.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
13.0ms	(* (log (hypot re im)) (log base))
52.0ms	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
3.0ms	(pow (log base) 2)

series615.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1))
104.0ms	(* (log (hypot re im)) (log base))
142.0ms	(* (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (/ 1 (/ (fma 0.0 0.0 (pow (log base) 2)) 1)))
154.0ms	(pow (log base) 2)

simplify88.0ms

Counts

226 → 226

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	817	2451
1	3669	2061
2	5002	1844
done	5002	1844

prune642.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	15
1	24	15
2	24	15
done	24	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

560.0ms	8000×	body	80	valid
555.0ms	7823×	body	80	nan