Details

sample151.0ms

Algorithm

intervals

Results

75.0ms	314×	body	80	nan
34.0ms	256×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize38.0ms

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))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

22.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
54.0ms	(/ (+ (* (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))
11.0ms	(sqrt (+ (* re re) (* im im)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
162.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
224.0ms	(* (log base) (log base))
48.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.1s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2906
1	507
0	200

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
0.6b	(pow (log base) 2)
0.6b	(* (log base) (log base))
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

89.0ms	(/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
3.0ms	(pow (log base) 2)
14.0ms	(* (log base) (log base))
7.0ms	(sqrt (+ (* re re) (* im im)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
220.0ms	(pow (log base) 2)
215.0ms	(* (log base) (log base))
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	2602
1	499
0	203

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
0.9b	(pow (log base) 4)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms	(* (log base) (log base))
4.0ms	(pow (log base) 4)
13.0ms	(sqrt (+ (* re re) (* im im)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
273.0ms	(* (log base) (log base))
292.0ms	(pow (log base) 4)
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5002
2	2518
1	401
0	155

prune1.3s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 5.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (log base) 2)
0.6b	(* (log base) (log base))
0.7b	(pow (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* 0.0 (atan2 im re))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) 3)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
28×	`unpow-prod-down`
24×	`cube-prod`
21×	`pow1` `sqrt-prod`
10×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`log-pow`
6×	`pow-unpow` `log-prod` `sqrt-div` `swap-sqr`
4×	`associate-r` `associate-l` `associate-/r/` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+`
2×	`pow-to-exp` `pow-pow` `div-inv` `rem-cube-cbrt` `sqr-pow`
1×	`cube-div` `pow2` `cube-mult` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `unpow3` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unpow2` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

5.0ms	(pow (log base) 2)
15.0ms	(* (log base) (log base))
41.0ms	(pow (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* 0.0 (atan2 im re))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) 3)
13.0ms	(sqrt (+ (* re re) (* im im)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(pow (log base) 2)
240.0ms	(* (log base) (log base))
138.0ms	(pow (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* 0.0 (atan2 im re))) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) 3)
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.2s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	4190
1	895
0	243

prune1.2s

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 4.7b

regimes1.2s

Accuracy

47.2% (14.9b remaining)

Error of 18.6b against oracle of 3.7b and baseline of 31.9b

bsearch633.0ms

Steps

Iters	Range		Point
10	117332107226.37881	6.552973658657202e+20	6.45957920562455e+20
8	3.4855366291793885e-176	3.901630353191231e-172	6.773165473524224e-176
9	5.8289788190227e-236	8.696307363036179e-231	2.521155375520642e-231
8	-769416.9694931002	-176.46382879882907	-732279.7988286485

simplify23.0ms

Iterations

Iter	Nodes
done	75
1	75
0	59

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	7990×	body	80	nan
1.3s	8000×	body	80	valid