Details

sample81.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
27.0ms	277×	body	80	nan

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize46.0ms

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))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite83.0ms

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))
42.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (log base) (log base))
13.0ms	(sqrt (+ (* re re) (* im im)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
164.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
220.0ms	(* (log base) (log base))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.5s

Counts

122 → 122

Iterations

Useful iterations: done (3.5s)

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

prune715.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.6b	(pow (log base) 2)
0.6b	(* (log base) (log base))
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 261

Calls

4 calls:

128.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
16.0ms	(pow (log base) 2)
17.0ms	(* (log base) (log base))
13.0ms	(sqrt (+ (* re re) (* im im)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
177.0ms	(pow (log base) 2)
173.0ms	(* (log base) (log base))
58.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts

273 → 273

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	417	14712
1	881	13094
2	1921	12399
done	5001	12041

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (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)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite238.0ms

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:

225.0ms	(/ (+ (* (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)
8.0ms	(sqrt (+ (* re re) (* im im)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (+ (* (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)))
209.0ms	(cbrt base)
233.0ms	(cbrt base)
67.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.2s

Counts

80 → 80

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	148	2200
1	369	2008
2	1172	1664
3	4679	1594
done	5001	1509

prune618.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 6.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
9×	`pow1`
8×	`add-exp-log` `unpow-prod-down`
6×	`pow-unpow` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `log-pow` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

55.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
8.0ms	(sqrt (+ (* re re) (* im im)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0))))
262.0ms	(pow (log base) 2)
212.0ms	(pow (log base) 2)
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

108 → 108

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	167	2516
1	366	2350
2	921	2199
3	2753	2173
done	5000	2169

prune644.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 5.7b

regimes1.5s

Accuracy

56.2% (11.1b remaining)

Error of 17.6b against oracle of 6.5b and baseline of 31.8b

bsearch451.0ms

Steps

Iters	Range		Point
10	1.6558114091021875e+84	3.809265903266752e+94	5.983180677799418e+93
3	3.8873671139371303e-295	4.984156002397002e-295	4.3520111321477895e-295
5	-5.565598515937264e-162	-2.5119663807524717e-162	-2.550928749919679e-162
8	-2.5792957900424365e+73	-1.632159520315139e+69	-1.860564632808157e+70

simplify25.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	147
1	86	147
done	86	147

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.9s	8045×	body	80	nan
1.4s	8000×	body	80	valid