Details

sample90.0ms

Algorithm

intervals

Results

42.0ms	256×	body	80	valid
25.0ms	232×	body	80	nan

simplify12.0ms

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: 30.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite112.0ms

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:

21.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
55.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
16.0ms	(* (log base) (log base))
17.0ms	(sqrt (+ (* re re) (* im im)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
153.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
216.0ms	(* (log base) (log base))
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify3.8s

Counts

122 → 122

Iterations

Useful iterations: done (3.8s)

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

prune739.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(pow (log base) 2)
0.5b	(* (log base) (log base))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`log-prod`
11×	`log-pow`
10×	`associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `pow-pow` `flip3-+` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

26.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
6.0ms	(pow (log base) 2)
19.0ms	(* (log base) (log base))
15.0ms	(sqrt (+ (* re re) (* im im)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
251.0ms	(pow (log base) 2)
230.0ms	(* (log base) (log base))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts

110 → 110

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	151	1213
1	295	1043
2	786	934
3	2442	902
done	5000	893

prune610.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
58×	`times-frac`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`pow1`
8×	`unpow-prod-down` `div-exp` `prod-exp`
6×	`pow-unpow` `sqrt-div`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp` `log-pow` `div-inv` `unpow2` `sqr-pow`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 140

Calls

4 calls:

163.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
6.0ms	(pow (log base) 2)
6.0ms	(pow (log base) 2)
15.0ms	(sqrt (+ (* re re) (* im im)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (/ 1 (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))) (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (pow (log base) 2) (* 0.0 0.0)))))
210.0ms	(pow (log base) 2)
212.0ms	(pow (log base) 2)
63.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts

152 → 152

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	235	5236
1	624	4886
2	2107	4095
done	5001	4080

prune889.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
0.9b	(pow (log base) 4)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `unpow-prod-down`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow-unpow`
7×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqrt-prod` `log-pow` `sqr-pow`
2×	`sqrt-div` `unpow2`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 71

Calls

4 calls:

6.0ms	(pow (log base) 2)
4.0ms	(pow (log base) 2)
12.0ms	(pow (log base) 4)
11.0ms	(sqrt (+ (* re re) (* im im)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(pow (log base) 2)
238.0ms	(pow (log base) 2)
232.0ms	(pow (log base) 4)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts

83 → 83

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	98	660
1	216	560
2	441	506
3	1418	491
done	5000	481

prune530.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.8b

regimes888.0ms

Accuracy

55.9% (10.8b remaining)

Error of 18.1b against oracle of 7.3b and baseline of 31.8b

bsearch425.0ms

Steps

Iters	Range		Point
7	8.712956771106514e+71	2.7708219827239753e+73	1.6681351351351405e+72
9	1.3411490674140207e-196	4.744880302659544e-190	1.9547532014272984e-192
10	-1.0825666046870533e-205	-2.1585574380706572e-215	-2.2053249985564832e-213
1	-4.90105109200061e+89	-4.6551667645331244e+89	-4.716637846399996e+89

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	49	116
1	60	114
2	63	114
done	63	114

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.0s	8000×	body	80	valid
1.3s	8016×	body	80	nan