Details

sample115.0ms

Algorithm

intervals

Results

40.0ms	284×	body	80	nan
30.0ms	256×	body	80	valid

simplify64.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize192.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (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))
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

127.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
60.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
44.0ms	(* (log base) (log base))
19.0ms	(sqrt (+ (* re re) (* im im)))

series819.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
235.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
299.0ms	(* (log base) (log base))
85.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.7s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1599
1	510
0	204

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize190.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`log-prod`
16×	`log-pow`
14×	`associate-l`
12×	`swap-sqr` `associate-r`
10×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 119

Calls

4 calls:

32.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
32.0ms	(* (log base) (log base))
22.0ms	(* (log base) (log base))
24.0ms	(sqrt (+ (* re re) (* im im)))

series813.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
278.0ms	(* (log base) (log base))
287.0ms	(* (log base) (log base))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify10.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	5003
4	4471
3	1798
2	757
1	316
0	133

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.4b

localize328.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
32.4b	(sqrt (+ (* re re) (* im im)))
32.4b	(sqrt (+ (* re re) (* im im)))
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

12.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
19.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
20.0ms	(sqrt (+ (* re re) (* im im)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
64.0ms	(sqrt (+ (* re re) (* im im)))
72.0ms	(sqrt (+ (* re re) (* im im)))
71.0ms	(sqrt (+ (* re re) (* im im)))

simplify5.9s

Counts

77 → 77

Iterations

Iter	Nodes
done	5004
4	3587
3	1020
2	342
1	149
0	72

prune1.3s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.4b

localize226.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt base)
0.6b	(cbrt base)
0.6b	(cbrt base)
32.4b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt base)
2.0ms	(cbrt base)
2.0ms	(cbrt base)
17.0ms	(sqrt (+ (* re re) (* im im)))

series837.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt base)
255.0ms	(cbrt base)
304.0ms	(cbrt base)
55.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
4	1516
3	617
2	285
1	132
0	62

prune755.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 7.3b

regimes2.1s

Accuracy

57.5% (10.7b remaining)

Error of 17.8b against oracle of 7.1b and baseline of 32.3b

bsearch582.0ms

Steps

Iters	Range		Point
6	2.47240381234954e+119	3.331204183500167e+120	7.02389227678964e+119
7	-4.23348094612349e-286	-4.623056101715811e-288	-6.019878598432241e-287
10	-2.1826079353971266e-191	-1.6446586965205068e-206	-3.60594831894126e-205
8	-2.344500353184379e+122	-1.4228774487393373e+118	-1.7816411661937366e+118

simplify82.0ms

Iterations

Iter	Nodes
done	79
4	79
3	75
2	70
1	68
0	52

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.9s	8090×	body	80	nan
1.5s	8000×	body	80	valid