Details

sample58.0ms

Algorithm

intervals

Results

22.0ms	260×	body	80	nan
18.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 31.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
148.0ms	(* (log base) (log base))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify736.0ms

Counts

122 → 122

Iterations

Useful iterations: done (732.0ms)

Iter	Nodes	Cost
0	200	2451
1	441	2259
2	1349	2035
done	5000	2023

prune531.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
0.6b	(cbrt base)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
6×	`add-exp-log` `cbrt-prod` `log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `log-pow` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

9.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0ms	(cbrt base)
1.0ms	(cbrt base)
4.0ms	(sqrt (+ (* re re) (* im im)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
186.0ms	(cbrt base)
185.0ms	(cbrt base)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

77 → 77

Iterations

Useful iterations: 4 (783.0ms)

Iter	Nodes	Cost
0	116	875
1	229	828
2	555	728
3	1255	707
4	2981	705
done	5000	705

prune432.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(cbrt base)
5.1b	(pow (/ 1 base) -1/3)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`unpow-prod-down`
12×	`pow1`
11×	`add-exp-log`
9×	`times-frac`
6×	`log-prod` `associate-l` `add-cbrt-cube`
4×	`associate-r` `pow-exp` `log-pow` `add-log-exp`
3×	`cbrt-prod` `distribute-rgt-in` `pow-unpow` `pow-pow` `distribute-lft-in` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-exp`
1×	`pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-flip` `flip3-+` `pow1/3` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `inv-pow` `unswap-sqr` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.0ms	(cbrt base)
4.0ms	(pow (/ 1 base) -1/3)
4.0ms	(sqrt (+ (* re re) (* im im)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
186.0ms	(cbrt base)
188.0ms	(pow (/ 1 base) -1/3)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.4s

Counts

98 → 98

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	184	1139
1	379	1033
2	803	927
3	1752	898
4	4941	892
done	5000	892

prune730.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

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:

24.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
7.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (+ (* 0.0 0.0) (pow (log base) 2)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
96.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(pow (log base) 2)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts

105 → 105

Iterations

Useful iterations: 3 (807.0ms)

Iter	Nodes	Cost
0	194	2235
1	442	2127
2	1237	1939
3	4499	1910
done	5000	1910

prune432.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.4b

regimes594.0ms

Accuracy

59.2% (10.0b remaining)

Error of 17.3b against oracle of 7.2b and baseline of 31.8b

bsearch161.0ms

Steps

Iters	Range		Point
9	1.8684288122828866e+141	1.3023166688765237e+147	1.978996135853368e+145
6	-7.134127296663583e+142	-6.065115406379256e+141	-9.507267753592183e+141

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	91
1	59	91
done	59	91

end0.0ms

sample1.5s

Algorithm

intervals

Results

586.0ms	8174×	body	80	nan
555.0ms	8000×	body	80	valid