Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
16.0ms	224×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	23	28
done	23	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
34.1b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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×	`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` `div-inv`

Counts

4 → 110

Calls

4 calls:

14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify759.0ms

Counts

122 → 122

Iterations

Useful iterations: done (751.0ms)

Iter	Nodes	Cost
0	200	2451
1	441	2259
2	1351	2035
done	5000	2023

prune503.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.5b	(pow (log base) 2)
0.5b	(* (log base) (log base))
34.1b	(sqrt (+ (* re re) (* im im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
157×	`add-sqr-sqrt`
156×	`*-un-lft-identity`
154×	`add-cube-cbrt`
141×	`sqrt-prod`
24×	`associate-/l*`
20×	`pow1`
18×	`sqrt-div`
16×	`associate-/r/`
12×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-inv`
7×	`log-pow`
6×	`log-prod` `swap-sqr` `associate-/r*`
4×	`unpow-prod-down` `associate-r` `associate-l` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `pow-unpow` `distribute-lft-in` `div-exp`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 261

Calls

4 calls:

43.0ms	(/ (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
1.0ms	(pow (log base) 2)
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
154.0ms	(pow (log base) 2)
150.0ms	(* (log base) (log base))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

273 → 273

Iterations

Useful iterations: 2 (608.0ms)

Iter	Nodes	Cost
0	417	14712
1	915	13208
2	2268	12413
done	5001	12413

prune840.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
34.1b	(sqrt (+ (* re re) (* im im)))
34.1b	(sqrt (+ (* re re) (* im im)))
34.1b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-plus`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 91

Calls

4 calls:

16.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base)))
42.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

103 → 103

Iterations

Useful iterations: 3 (715.0ms)

Iter	Nodes	Cost
0	125	2176
1	304	1955
2	910	1564
3	3019	1483
done	5001	1483

prune442.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
34.1b	(sqrt (+ (* re re) (* im im)))
34.1b	(sqrt (+ (* re re) (* im im)))
34.1b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `log-pow` `unpow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

1.0ms	(pow (log base) 2)
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))
42.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.3s

Counts

76 → 76

Iterations

Useful iterations: 4 (992.0ms)

Iter	Nodes	Cost
0	74	788
1	169	683
2	371	618
3	1005	597
4	4088	593
done	5001	593

prune347.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.5b

regimes628.0ms

Accuracy

54.8% (11.1b remaining)

Error of 18.7b against oracle of 7.6b and baseline of 32.1b

bsearch262.0ms

Steps

Iters	Range		Point
10	1.502402743307226e+92	1.2907170496906384e+102	6.977573052836996e+98
5	-1.0159098064350865e-242	-2.897696440015651e-243	-9.888558650632372e-243
6	-8.938153707479813e-161	-1.4661440321995653e-161	-2.3495244626294698e-161
5	-1.3410726593209138e+125	-5.30850989712408e+124	-1.2179686555766433e+125

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	179
1	63	179
done	63	179

end0.0ms

sample1.6s

Algorithm

intervals

Results

689.0ms	8000×	body	80	valid
546.0ms	7961×	body	80	nan