Details

sample120.0ms

Algorithm

intervals

Results

53.0ms	273×	body	80	nan
44.0ms	256×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	22
1	22
0	18

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
20×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
12×	`log-prod`
10×	`associate-l` `log-pow`
8×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `flip3-+` `times-frac` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `associate-/l`

Counts

4 → 104

Calls

4 calls:

24.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
20.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
142.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
241.0ms	(* (log base) (log base))
54.0ms	(sqrt (+ (* re re) (* im im)))

simplify8.8s

Counts

116 → 116

Iterations

Iter	Nodes
3	11790
2	1707
1	417
0	162

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
0.4b	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
94×	`log-pow`
90×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
78×	`pow1`
34×	`associate-/r*`
22×	`sqrt-pow1` `pow1/2`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
3×	`sqrt-prod` `insert-posit16` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `sqrt-div` `1-exp`
1×	`rem-sqrt-square` `flip3-+` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

3 → 200

Calls

3 calls:

7.0ms	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
7.0ms	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))

series408.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(/ 1 (/ (log base) (log (sqrt (+ (* re re) (* im im))))))
171.0ms	(/ (log base) (log (sqrt (+ (* re re) (* im im)))))
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.6s

Counts

209 → 209

Iterations

Iter	Nodes
3	3681
2	1503
1	575
0	244

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (log (sqrt (+ (* re re) (* im im)))) (log base)))
0.3b	(/ 1 (/ 1 (/ (log (sqrt (+ (* re re) (* im im)))) (log base))))
0.4b	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

1095×	`times-frac`
429×	`add-sqr-sqrt`
428×	`*-un-lft-identity` `add-cube-cbrt`
310×	`log-pow`
249×	`pow1`
121×	`associate-/r*`
70×	`sqrt-pow1` `pow1/2`
60×	`add-exp-log`
43×	`div-exp`
23×	`div-inv`
20×	`add-cbrt-cube`
15×	`rec-exp` `1-exp`
12×	`associate-/l*`
10×	`cbrt-undiv`
6×	`associate-/r/`
5×	`pow-flip`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod` `inv-pow`
2×	`log-div` `flip3-+` `div-sub` `flip-+`
1×	`rem-sqrt-square` `remove-double-div`

Counts

4 → 602

Calls

4 calls:

7.0ms	(/ 1 (/ (log (sqrt (+ (* re re) (* im im)))) (log base)))
11.0ms	(/ 1 (/ 1 (/ (log (sqrt (+ (* re re) (* im im)))) (log base))))
25.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1 (/ (log (sqrt (+ (* re re) (* im im)))) (log base)))
116.0ms	(/ 1 (/ 1 (/ (log (sqrt (+ (* re re) (* im im)))) (log base))))
97.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify31.2s

Counts

614 → 614

Iterations

Iter	Nodes
2	2541
1	1577
0	596

prune2.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
0.3b	(/ 1 (log base))
0.3b	(/ (/ 1 (log base)) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

964×	`times-frac`
380×	`add-sqr-sqrt`
379×	`*-un-lft-identity` `add-cube-cbrt`
238×	`log-pow`
190×	`pow1`
56×	`sqrt-pow1` `pow1/2`
52×	`add-exp-log`
43×	`div-inv`
36×	`div-exp`
32×	`associate-/r*`
22×	`associate-/l*`
20×	`add-cbrt-cube`
10×	`cbrt-undiv` `rec-exp` `1-exp`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod`
2×	`sqrt-div` `pow-flip` `inv-pow`
1×	`rem-sqrt-square` `flip3-+` `associate-/r/` `flip-+` `associate-/l/`

Counts

4 → 519

Calls

4 calls:

4.0ms	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
4.0ms	(/ 1 (log base))
12.0ms	(/ (/ 1 (log base)) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
17.0ms	(sqrt (+ (* re re) (* im im)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (log (sqrt (+ (* re re) (* im im)))))
248.0ms	(/ 1 (log base))
126.0ms	(/ (/ 1 (log base)) (/ 1 (log (sqrt (+ (* re re) (* im im))))))
70.0ms	(sqrt (+ (* re re) (* im im)))

simplify8.2s

Counts

531 → 531

Iterations

Iter	Nodes
2	3018
1	1696
0	570

prune1.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.0b

regimes587.0ms

Accuracy

57.4% (10.0b remaining)

Error of 17.3b against oracle of 7.4b and baseline of 30.7b

bsearch567.0ms

Steps

Iters	Range		Point
10	3.483388077252769e+90	7.103223856705159e+101	7.000536400588895e+101
7	-1.669117216904853e-227	-8.788432982908868e-229	-7.929293363153046e-228
9	-1.3759682400933023e-147	-4.483855952486962e-157	-4.573649974847702e-157
11	-8.738231427218701e+132	-8.486041932179183e+111	-2.6939147341520852e+126

simplify10.0ms

Iterations

Iter	Nodes
2	39
1	39
0	36

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	7969×	body	80	nan
1.9s	8000×	body	80	valid