Details

sample137.0ms

Algorithm

intervals

Results

61.0ms	270×	body	80	nan
53.0ms	256×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5430
8	1158
7	369
6	195
5	101
4	53
3	39
2	24
1	22
0	18

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt (+ (* re re) (* im im))))
0.3b	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

25×	`log-pow`
24×	`times-frac`
23×	`pow1`
19×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-pow1` `pow1/2`
6×	`log-prod` `sqrt-div` `add-exp-log` `sqrt-prod` `associate-/l*`
5×	`add-cbrt-cube`
4×	`log-div` `associate-/r*`
3×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
2×	`div-sub`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv`

Counts

3 → 85

Calls

3 calls:

9.0ms	(log (sqrt (+ (* re re) (* im im))))
37.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms	(sqrt (+ (* re re) (* im im)))

series218.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(log (sqrt (+ (* re re) (* im im))))
98.0ms	(/ (log (sqrt (+ (* re re) (* im im)))) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
4	2539
3	1175
2	508
1	247
0	134

prune424.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

localize29.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* 1/2 (log (+ (* re re) (* im im)))) (log base))
32.4b	(log (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-/r*` `times-frac`
3×	`log-prod` `log-pow`
2×	`cbrt-undiv` `log-div` `div-exp` `insert-posit16` `add-log-exp`
1×	`clear-num` `frac-2neg` `flip3-+` `rem-log-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

2 → 39

Calls

2 calls:

29.0ms	(/ (* 1/2 (log (+ (* re re) (* im im)))) (log base))
8.0ms	(log (+ (* re re) (* im im)))

series179.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(/ (* 1/2 (log (+ (* re re) (* im im)))) (log base))
71.0ms	(log (+ (* re re) (* im im)))

simplify2.0s

Counts

45 → 45

Iterations

Iter	Nodes
done	5006
3	2648
2	675
1	248
0	104

prune240.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.6b

localize39.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 1 (log base))
0.3b	(* (* 1/2 (log (+ (* re re) (* im im)))) (/ 1 (log base)))
32.4b	(log (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
24×	`times-frac`
21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`pow1` `add-cbrt-cube`
16×	`associate-r`
12×	`prod-exp`
8×	`log-pow`
6×	`div-exp` `cbrt-unprod`
4×	`associate-/r*`
3×	`cbrt-undiv` `rec-exp` `log-prod` `1-exp` `pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`log-div` `div-inv`
1×	`clear-num` `frac-2neg` `flip3-+` `rem-log-exp` `associate-l` `associate-r/` `un-div-inv` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

3 → 93

Calls

3 calls:

6.0ms	(/ 1 (log base))
29.0ms	(* (* 1/2 (log (+ (* re re) (* im im)))) (/ 1 (log base)))
8.0ms	(log (+ (* re re) (* im im)))

series341.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(/ 1 (log base))
105.0ms	(* (* 1/2 (log (+ (* re re) (* im im)))) (/ 1 (log base)))
70.0ms	(log (+ (* re re) (* im im)))

simplify2.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3429
2	1090
1	370
0	152

prune431.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (/ 1/8 (* (/ (log base) (log (+ (* re re) (* im im)))) (/ (log base) (log (+ (* re re) (* im im)))))) (/ (log base) (log (+ (* re re) (* im im))))))
32.4b	(log (+ (* re re) (* im im)))
32.4b	(log (+ (* re re) (* im im)))
32.4b	(log (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

420×	`times-frac`
205×	`cbrt-prod`
138×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
87×	`pow1`
83×	`log-pow`
61×	`associate-/r/`
31×	`div-inv`
20×	`frac-times` `associate-l/` `associate-r/`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
1×	`cbrt-div` `pow1/3`

Counts

4 → 260

Calls

4 calls:

10.0ms	(cbrt (/ (/ 1/8 (* (/ (log base) (log (+ (* re re) (* im im)))) (/ (log base) (log (+ (* re re) (* im im)))))) (/ (log base) (log (+ (* re re) (* im im))))))
5.0ms	(log (+ (* re re) (* im im)))
6.0ms	(log (+ (* re re) (* im im)))
5.0ms	(log (+ (* re re) (* im im)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (/ (/ 1/8 (* (/ (log base) (log (+ (* re re) (* im im)))) (/ (log base) (log (+ (* re re) (* im im)))))) (/ (log base) (log (+ (* re re) (* im im))))))
52.0ms	(log (+ (* re re) (* im im)))
49.0ms	(log (+ (* re re) (* im im)))
53.0ms	(log (+ (* re re) (* im im)))

simplify2.1s

Counts

272 → 272

Iterations

Iter	Nodes
done	5004
2	3732
1	1248
0	592

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.5b

regimes502.0ms

Accuracy

58.1% (10.0b remaining)

Error of 17.4b against oracle of 7.4b and baseline of 31.2b

bsearch209.0ms

Steps

Iters	Range		Point
8	1.3252953297811756e+38	6.68994686148466e+41	3.913600501226428e+41
4	-5.865749711028935e+93	-3.0020127974286287e+93	-5.235503805450076e+93

simplify8.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	7673×	body	80	nan
1.9s	8000×	body	80	valid