Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7
done	11	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
0.6b	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`log-pow`
24×	`times-frac`
23×	`pow1`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
7×	`sqrt-pow1` `pow1/2`
6×	`add-exp-log` `log-prod` `sqrt-div` `sqrt-prod` `associate-/l*`
5×	`add-cbrt-cube`
4×	`log-div` `associate-/r*`
3×	`flip3-+` `flip-+` `add-log-exp`
2×	`div-sub`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

3 → 82

Calls

3 calls:

10.0ms	(log (sqrt (+ (* re re) (* im im))))
28.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
8.0ms	(sqrt (+ (* re re) (* im im)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(log (sqrt (+ (* re re) (* im im))))
137.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log 10.0))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify166.0ms

Counts

91 → 91

Iterations

Useful iterations: 4 (158.0ms)

Iter	Nodes	Cost
0	231	848
1	574	794
2	1350	791
3	4699	791
4	5001	790
done	5001	790

prune281.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
32.9b	(log (+ (* re re) (* im im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac`
82×	`add-sqr-sqrt`
54×	`sqrt-prod`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1`
32×	`associate-r`
28×	`log-pow`
25×	`associate-l`
18×	`add-exp-log`
17×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp`
4×	`log-div` `prod-exp` `cbrt-unprod` `associate-/l*`
3×	`log-prod` `div-inv` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 153

Calls

3 calls:

48.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
24.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
7.0ms	(log (+ (* re re) (* im im)))

series390.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(* (/ 1/2 (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
196.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
54.0ms	(log (+ (* re re) (* im im)))

simplify61.0ms

Counts

162 → 162

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	528	2082
1	2065	1915
2	5001	1832
done	5001	1832

prune392.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.4b

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
1.0b	(sqrt (sqrt (log 10.0)))
1.0b	(sqrt (sqrt (log 10.0)))
32.9b	(log (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
60×	`times-frac`
56×	`add-sqr-sqrt`
52×	`add-cube-cbrt` `*-un-lft-identity`
33×	`cbrt-prod`
18×	`pow1`
10×	`associate-/r*` `log-pow`
8×	`sqrt-pow1`
7×	`add-exp-log`
6×	`associate-/l*`
5×	`add-cbrt-cube`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
3×	`log-prod`
2×	`log-div`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 142

Calls

4 calls:

10.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
3.0ms	(sqrt (sqrt (log 10.0)))
3.0ms	(sqrt (sqrt (log 10.0)))
7.0ms	(log (+ (* re re) (* im im)))

series56.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(/ (cbrt 1/2) (sqrt (sqrt (log 10.0))))
0.0ms	(sqrt (sqrt (log 10.0)))
0.0ms	(sqrt (sqrt (log 10.0)))
56.0ms	(log (+ (* re re) (* im im)))

simplify54.0ms

Counts

148 → 148

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	280	1323
1	641	1272
2	1678	1195
3	5001	1183
done	5001	1183

prune465.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
0.5b	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
0.5b	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
32.9b	(log (+ (* re re) (* im im)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
131×	`add-sqr-sqrt`
107×	`sqrt-prod`
79×	`add-cube-cbrt` `*-un-lft-identity`
78×	`add-exp-log`
68×	`associate-l`
59×	`add-cbrt-cube`
42×	`pow1`
33×	`associate-r`
31×	`prod-exp` `log-pow`
27×	`div-exp`
22×	`cbrt-unprod`
18×	`cbrt-undiv`
15×	`unswap-sqr`
7×	`associate-/r*`
6×	`frac-times` `associate-*r/`
5×	`1-exp`
4×	`log-div` `pow-prod-down` `associate-l/` `div-inv` `associate-/l` `add-log-exp`
3×	`log-prod`
2×	`flip3-+` `div-sub` `*-commutative` `flip-+`
1×	`frac-2neg` `rem-log-exp` `clear-num`

Counts

4 → 245

Calls

4 calls:

60.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
71.0ms	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
25.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
7.0ms	(log (+ (* re re) (* im im)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0))))
239.0ms	(* (/ (sqrt 1/2) 1) (* (/ (sqrt 1/2) (sqrt (log 10.0))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))))
200.0ms	(/ (log (+ (* re re) (* im im))) (sqrt (log 10.0)))
51.0ms	(log (+ (* re re) (* im im)))

simplify113.0ms

Counts

257 → 257

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	888	3877
1	4541	3356
2	5001	3222
done	5001	3222

prune614.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 9.3b

regimes613.0ms

Accuracy

58.2% (10.4b remaining)

Error of 17.7b against oracle of 7.3b and baseline of 32.1b

bsearch188.0ms

Steps

Iters	Range		Point
8	1.0656776998337841e+73	2.1069570435261278e+76	1.2665214372256669e+76
8	-8.88757827843957e-288	-5.138571342544288e-291	-2.4372997740340113e-288
8	-1.3689810004075542e-219	-2.7055579969198535e-224	-4.371006412922919e-223
9	-2.779170551787003e+126	-7.0065691084106e+119	-8.528127276764349e+119

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	80
1	71	80
done	71	80

end0.0ms

sample536.0ms

Algorithm

intervals

Results

349.0ms

8000×

body

valid