Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	242×	body	80	nan
17.0ms	256×	body	80	valid

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: 32.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite73.0ms

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:

13.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
39.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
8.0ms	(sqrt (+ (* re re) (* im im)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
104.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
150.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (48.0ms)

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

prune473.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(* (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))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

0.0ms	(hypot re im)
9.0ms	(* (log (hypot re im)) (log base))
35.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
9.0ms	(* (log base) (log base))

series417.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
104.0ms	(* (log (hypot re im)) (log base))
114.0ms	(/ (+ (* (log (hypot re im)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
153.0ms	(* (log base) (log base))

simplify56.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	394	1062
1	1578	951
2	5002	926
done	5002	926

prune397.0ms

Pruning

13 alts after pruning (13 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))
0.3b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
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)))

rewrite80.0ms

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))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
7.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
49.0ms	(* (/ 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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

337.0ms	(/ 1 (/ (hypot (log base) 0.0) 1))
104.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
306.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (* (hypot (log base) 0.0) 1))
353.0ms	(* (/ 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)))

simplify95.0ms

Counts

248 → 248

Iterations

Useful iterations: 2 (66.0ms)

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

prune630.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) (* 2 2)))) 2) (- (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) (* 2 2))))
0.6b	(* (log base) (log base))
0.9b	(pow (log base) (* 2 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`add-exp-log`
25×	`add-cbrt-cube`
24×	`pow1`
18×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
13×	`associate-/l*`
12×	`associate--l+`
8×	`associate-r` `prod-exp` `cbrt-unprod`
7×	`log-pow`
6×	`cbrt-undiv` `swap-sqr` `div-exp`
5×	`associate-l` `div-inv`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`frac-times` `sub-neg` `flip3--` `associate-r/` `prod-diff` `-commutative` `flip--`
1×	`pow2` `pow-to-exp` `pow-unpow` `pow-pow` `frac-2neg` `pow-plus` `pow-exp` `clear-num` `pow-sqr` `pow-prod-up` `associate-/l/` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 176

Calls

4 calls:

70.0ms	(* (* (/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) (* 2 2)))) 2) (- (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) (* 2 2))))
9.0ms	(* (log base) (log base))
4.0ms	(pow (log base) (* 2 2))

series707.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (* (/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) (* 2 2)))) 2) (- (* (log base) (log base)) (* 0.0 0.0)))
181.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 2) (fma (- (pow 0.0 3)) 0.0 (pow (log base) (* 2 2))))
145.0ms	(* (log base) (log base))
157.0ms	(pow (log base) (* 2 2))

simplify136.0ms

Counts

188 → 188

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	890	3486
1	4628	3159
2	5001	3159
done	5001	3159

prune802.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes207.0ms

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

567.0ms	8215×	body	80	nan
541.0ms	8000×	body	80	valid