Details

sample106.0ms

Algorithm

intervals

Results

38.0ms	256×	body	80	valid
34.0ms	224×	body	80	nan

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize84.0ms

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))
24.0b	(sqrt (+ (* re re) (* im im)))

rewrite122.0ms

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))
69.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
20.0ms	(* (log base) (log base))
16.0ms	(sqrt (+ (* re re) (* im im)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
223.0ms	(* (log base) (log base))
65.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.3s

Counts

122 → 122

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	200	2451
1	442	2259
2	1344	2035
3	4400	1998
done	5000	1992

prune670.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b	(pow (log base) 2)
24.0b	(sqrt (+ (* re re) (* im im)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
6×	`log-prod` `associate-l`
5×	`log-pow`
4×	`unpow-prod-down` `associate-r` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
81.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
5.0ms	(pow (log base) 2)
16.0ms	(sqrt (+ (* re re) (* im im)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
206.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
252.0ms	(pow (log base) 2)
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.5s

Counts

105 → 105

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	194	2235
1	438	2123
2	1249	1937
3	4242	1910
done	5001	1908

prune714.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 6.0b

localize49.0ms

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)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
0.5b	(pow (log base) 2)
24.0b	(sqrt (+ (* re re) (* im im)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`associate-l`
6×	`log-prod`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

14.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
93.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
6.0ms	(pow (log base) 2)
16.0ms	(sqrt (+ (* re re) (* im im)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
177.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
235.0ms	(pow (log base) 2)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

116 → 116

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	225	2560
1	551	2351
2	1701	2090
done	5000	2065

prune678.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 6.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (- (pow (log base) 4) (* 0.0 (pow 0.0 3)))) (- (pow (log base) 2) (* 0.0 0.0)))
0.5b	(pow (log base) 2)
0.8b	(pow (log base) 4)
24.0b	(sqrt (+ (* re re) (* im im)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-l`
11×	`pow1` `add-exp-log`
10×	`times-frac`
9×	`unpow-prod-down` `add-cbrt-cube`
7×	`associate-r`
6×	`pow-unpow`
4×	`add-log-exp` `difference-of-squares`
3×	`flip3--` `sqrt-prod` `flip--` `sqr-pow`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `sqrt-div` `associate-*r/` `pow-exp` `prod-exp` `associate-/r/` `log-pow` `cbrt-unprod` `unpow2` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

170.0ms	(* (/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (- (pow (log base) 4) (* 0.0 (pow 0.0 3)))) (- (pow (log base) 2) (* 0.0 0.0)))
3.0ms	(pow (log base) 2)
11.0ms	(pow (log base) 4)
11.0ms	(sqrt (+ (* re re) (* im im)))

series823.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (/ (+ (* (atan2 im re) 0.0) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (- (pow (log base) 4) (* 0.0 (pow 0.0 3)))) (- (pow (log base) 2) (* 0.0 0.0)))
314.0ms	(pow (log base) 2)
279.0ms	(pow (log base) 4)
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

110 → 110

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	214	2769
1	542	2646
2	1811	2263
done	5002	2102

prune852.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 0.3b

regimes646.0ms

Accuracy

46.5% (16.4b remaining)

Error of 16.8b against oracle of 0.3b and baseline of 31.0b

bsearch213.0ms

Steps

Iters	Range		Point
9	1.8488019868481542e+78	1.0001610251731045e+84	8.322808950963171e+83
7	-5.1690567046898904e+150	-8.581624916537611e+148	-8.699527506903107e+148

simplify16.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	38	54
1	49	52
2	52	52
done	52	52

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.7s	7907×	body	80	nan
1.3s	8000×	body	80	valid