Details

sample73.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
23.0ms	248×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite135.0ms

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:

15.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
78.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
21.0ms	(* (log base) (log base))
17.0ms	(sqrt (+ (* re re) (* im im)))

series649.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
169.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
283.0ms	(* (log base) (log base))
44.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: done (2.6s)

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

prune789.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite198.0ms

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:

146.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
27.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms	(pow (log base) 2)
16.0ms	(sqrt (+ (* re re) (* im im)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (pow (log base) 2) (* 0.0 0.0))))
148.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
293.0ms	(pow (log base) 2)
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify6.4s

Counts

116 → 116

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	225	2560
1	632	2395
2	4111	2097
done	5000	2097

prune661.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite120.0ms

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:

70.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
28.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(pow (log base) 2)
15.0ms	(sqrt (+ (* re re) (* im im)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
126.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
256.0ms	(pow (log base) 2)
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

105 → 105

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	194	2235
1	495	2124
2	1965	1940
done	5000	1926

prune579.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (pow (log base) 2) (* 0.0 0.0)) (/ 1 (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0))))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite183.0ms

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:

125.0ms	(* (+ (pow (log base) 2) (* 0.0 0.0)) (/ 1 (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0))))
23.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms	(pow (log base) 2)
25.0ms	(sqrt (+ (* re re) (* im im)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (+ (pow (log base) 2) (* 0.0 0.0)) (/ 1 (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0))))
135.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
265.0ms	(pow (log base) 2)
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.8s

Counts

116 → 116

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	225	2490
1	632	2317
2	4145	2017
done	5000	2017

prune531.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 6.5b

regimes742.0ms

Accuracy

57.3% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 32.0b

bsearch484.0ms

Steps

Iters	Range		Point
8	1.6378069706072204e+112	5.069416923494263e+114	2.796818833373207e+113
7	2.3571505250649092e-291	7.117929345426062e-290	4.104056990699005e-290
9	-2.8722041982661196e-234	-2.0414935290891285e-240	-1.0344052319582197e-234
11	-1.764296119965087e+115	-2.180461784664947e+87	-5.376053604410897e+96

simplify17.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	46	96
1	57	94
2	63	94
3	65	94
done	65	94

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
1.1s	7721×	body	80	nan