Details

sample137.0ms

Algorithm

intervals

Results

46.0ms	254×	body	80	nan
43.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite621.0ms

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:

31.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
539.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
25.0ms	(* (log base) (log base))
17.0ms	(sqrt (+ (* re re) (* im im)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
192.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
305.0ms	(* (log base) (log base))
73.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

122 → 122

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	200	2451
1	508	2278
2	2908	2038
done	5002	2023

prune983.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

221.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
5.0ms	(pow (log base) 2)
5.0ms	(pow (log base) 2)
13.0ms	(sqrt (+ (* re re) (* im im)))

series872.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
308.0ms	(pow (log base) 2)
262.0ms	(pow (log base) 2)
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.6s

Counts

152 → 152

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	235	5236
1	732	4980
2	4767	4430
done	5000	4430

prune1.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (* 2 (log (cbrt base))) (log base)) (* (log (cbrt base)) (log base))) (* 0.0 0.0)))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`pow1/3` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

216.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (* 2 (log (cbrt base))) (log base)) (* (log (cbrt base)) (log base))) (* 0.0 0.0)))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
15.0ms	(sqrt (+ (* re re) (* im im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

348.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (* 2 (log (cbrt base))) (log base)) (* (log (cbrt base)) (log base))) (* 0.0 0.0)))
309.0ms	(cbrt base)
292.0ms	(cbrt base)
53.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	148	2200
1	378	2008
2	1362	1792
done	5000	1689

prune1.0s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 7.0b

localize127.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(* (pow (log base) 2) (pow (log base) 2))
0.8b	(pow (pow (log base) 2) 3)
29.0b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

49×	`unpow-prod-down`
37×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`add-exp-log`
16×	`unswap-sqr` `sqr-pow`
15×	`pow1` `unpow2`
11×	`swap-sqr` `pow-exp`
9×	`pow-to-exp` `cube-prod` `associate-r` `associate-l` `prod-exp` `log-pow`
7×	`add-cbrt-cube`
6×	`pow-unpow`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow-pow` `sqrt-div`
1×	`pow2` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `rem-cube-cbrt`

Counts

4 → 138

Calls

4 calls:

6.0ms	(pow (log base) 2)
48.0ms	(* (pow (log base) 2) (pow (log base) 2))
12.0ms	(pow (pow (log base) 2) 3)
15.0ms	(sqrt (+ (* re re) (* im im)))

series1.1s

Counts

4 → 12

Calls

4 calls:

310.0ms	(pow (log base) 2)
316.0ms	(* (pow (log base) 2) (pow (log base) 2))
374.0ms	(pow (pow (log base) 2) 3)
61.0ms	(sqrt (+ (* re re) (* im im)))

simplify12.8s

Counts

150 → 150

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	160	1754
1	458	1196
2	3723	965
done	5000	965

prune1.6s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 7.0b

regimes1.8s

Accuracy

58% (10.4b remaining)

Error of 17.9b against oracle of 7.5b and baseline of 32.2b

bsearch761.0ms

Steps

Iters	Range		Point
9	1.7574403162226e+100	1.869754062292705e+107	5.037031638582551e+101
9	-7.556856097197653e-296	-1.1202972634220416e-300	-5.526674152994974e-299
8	-2.7643530385105938e-238	-2.70424046949253e-241	-9.75555317653938e-240
5	-4.4344687316459745e+145	-1.4374651696982963e+145	-1.9762771458899918e+145

simplify41.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	194
1	93	194
2	97	194
3	101	194
done	101	194

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.4s	7942×	body	80	nan
1.7s	8000×	body	80	valid