Details

sample813.0ms

Algorithm

intervals

Results

713.0ms	268×	body	80	nan
53.0ms	256×	body	80	valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
1	23
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize72.0ms

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))
0.6b	(* (log base) (log base))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite178.0ms

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:

79.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
29.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
20.0ms	(* (log base) (log base))
43.0ms	(sqrt (+ (* re re) (* im im)))

series794.0ms

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)))
184.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
338.0ms	(* (log base) (log base))
73.0ms	(sqrt (+ (* re re) (* im im)))

simplify4.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1673
1	506
0	200

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite103.0ms

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-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `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 → 115

Calls

4 calls:

27.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
30.0ms	(* (log base) (log base))
21.0ms	(* (log base) (log base))
19.0ms	(sqrt (+ (* re re) (* im im)))

series1.4s

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
466.0ms	(* (log base) (log base))
532.0ms	(* (log base) (log base))
66.0ms	(sqrt (+ (* re re) (* im im)))

simplify9.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5003
4	4400
3	1730
2	764
1	312
0	130

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.1b

localize89.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(* (log base) (log base))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
25×	`pow1`
23×	`add-cube-cbrt` `associate-r`
17×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod`
11×	`times-frac`
10×	`log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`flip3-+` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `div-inv`

Counts

4 → 121

Calls

4 calls:

154.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
29.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
20.0ms	(* (log base) (log base))
16.0ms	(sqrt (+ (* re re) (* im im)))

series2.3s

Counts

4 → 12

Calls

4 calls:

852.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* (log base) (log base)) (* 0.0 0.0))))
666.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
558.0ms	(* (log base) (log base))
164.0ms	(sqrt (+ (* re re) (* im im)))

simplify9.7s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2482
1	636
0	230

prune2.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.1b

localize195.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt base)
0.5b	(cbrt base)
0.5b	(cbrt base)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt base)
1.0ms	(cbrt base)
1.0ms	(cbrt base)
38.0ms	(sqrt (+ (* re re) (* im im)))

series3.6s

Counts

4 → 12

Calls

4 calls:

968.0ms	(cbrt base)
693.0ms	(cbrt base)
1.9s	(cbrt base)
73.0ms	(sqrt (+ (* re re) (* im im)))

simplify14.4s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
5	4432
4	1382
3	602
2	283
1	131
0	60

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.1b

regimes3.2s

Accuracy

59.8% (10.2b remaining)

Error of 17.6b against oracle of 7.4b and baseline of 32.8b

bsearch1.5s

Steps

Iters	Range		Point
7	1.0227581927339955e+126	5.061070997306893e+127	1.3369019524202937e+126
9	4.6954333836046016e-290	2.4479137313065226e-283	8.706440568089371e-287
9	-2.236028651311912e-187	-2.8964313419080864e-192	-5.466683203640612e-192
4	-1.071997153553084e+105	-7.133916773961665e+104	-1.038377890163373e+105

simplify48.0ms

Iterations

Iter	Nodes
done	69
4	69
3	65
2	60
1	56
0	45

end0.0ms

sample17.6s

Algorithm

intervals

Results

9.6s	8060×	body	80	nan
7.0s	8000×	body	80	valid