Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	238×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 33.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (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))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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:

14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
152.0ms	(* (log base) (log base))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify739.0ms

Counts

122 → 122

Iterations

Useful iterations: done (736.0ms)

Iter	Nodes	Cost
0	200	2451
1	441	2259
2	1349	2035
done	5000	2023

prune506.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
12×	`log-prod`
9×	`sqrt-prod`
8×	`add-exp-log` `unpow-prod-down`
6×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-r` `log-pow` `add-cbrt-cube`
4×	`associate-l` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
1.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (log base) (log (sqrt (+ (* re re) (* im im)))))
157.0ms	(pow (log base) 2)
155.0ms	(pow (log base) 2)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

99 → 99

Iterations

Useful iterations: 3 (659.0ms)

Iter	Nodes	Cost
0	132	1182
1	266	1069
2	727	945
3	2620	928
done	5001	928

prune429.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (log base) 2)
0.6b	(pow (log base) 2)
31.4b	(sqrt (+ (* re re) (* im im)))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
6×	`add-exp-log` `pow-unpow` `sqrt-prod`
4×	`sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `log-pow` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

2.0ms	(pow (log base) 2)
2.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (log base) 2)
155.0ms	(pow (log base) 2)
41.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

80 → 80

Iterations

Useful iterations: 4 (859.0ms)

Iter	Nodes	Cost
0	74	724
1	168	622
2	370	556
3	994	538
4	4059	530
done	5000	530

prune438.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b	(pow (log base) 2)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-r`
16×	`add-exp-log`
14×	`pow1`
11×	`times-frac` `add-cbrt-cube`
9×	`associate-l`
6×	`log-prod`
5×	`prod-exp` `log-pow`
4×	`unpow-prod-down` `flip3-+` `flip-+` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `rec-exp` `pow-pow` `1-exp` `associate-*r/` `pow-exp` `un-div-inv` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

39.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
1.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (/ 1 (+ (* 0.0 0.0) (pow (log base) 2))))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(pow (log base) 2)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify851.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (286.0ms)

Iter	Nodes	Cost
0	225	2560
1	562	2351
2	1657	2090
done	5000	2090

prune415.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.9b

regimes440.0ms

Accuracy

57.8% (10.5b remaining)

Error of 17.6b against oracle of 7.1b and baseline of 32.0b

bsearch352.0ms

Steps

Iters	Range		Point
9	7.001991230040005e+100	5.286434132095145e+107	3.129365053182262e+107
10	5.746041526136169e-199	9.908015287167728e-184	6.310996251921044e-197
12	-1.6494711226975678e-177	-3.3431101685666744e-226	-7.729602790714112e-226
7	-1.7362790827402842e+99	-3.6356940138496794e+97	-8.25293219693442e+97

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	155
1	68	155
done	68	155

end0.0ms

sample1.5s

Algorithm

intervals

Results

566.0ms	7982×	body	80	nan
562.0ms	8000×	body	80	valid