Details

sample76.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
24.0ms	244×	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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.1b

Counts

2 → 1

localize20.0ms

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))
29.6b	(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:

6.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
11.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
7.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
31.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
17.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify466.0ms

Counts

122 → 122

Iterations

Useful iterations: done (462.0ms)

Iter	Nodes	Cost
0	203	2483
1	464	2346
2	1487	2089
done	5000	2022

prune274.0ms

Filtered

85 candidates to 122 candidates (-43.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	14	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 7.0b

Counts

123 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
0.5b	(pow (log base) 2)
0.5b	(pow (log base) 2)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite49.0ms

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:

32.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
3.0ms	(pow (log base) 2)
3.0ms	(pow (log base) 2)
4.0ms	(sqrt (+ (* re re) (* im im)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ 1 (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))) (/ (+ (* (atan2 im re) 0.0) (* (log base) (log (sqrt (+ (* re re) (* im im)))))) (sqrt (+ (* 0.0 0.0) (pow (log base) 2)))))
21.0ms	(pow (log base) 2)
16.0ms	(pow (log base) 2)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify809.0ms

Counts

152 → 152

Iterations

Useful iterations: done (803.0ms)

Iter	Nodes	Cost
0	240	5261
1	681	4967
2	2937	4177
done	5000	4095

prune409.0ms

Filtered

90 candidates to 152 candidates (-68.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	149	17	166

Merged error: 6.9b

Counts

166 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
0.5b	(cbrt (pow (log base) 6))
1.2b	(pow (log base) 6)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`pow1` `cbrt-prod` `unpow-prod-down`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
2×	`sqrt-div` `associate-/r/` `log-pow` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

14.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
2.0ms	(cbrt (pow (log base) 6))
3.0ms	(pow (log base) 6)
4.0ms	(sqrt (+ (* re re) (* im im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (cbrt (pow (log base) 6)) (* 0.0 0.0)))
19.0ms	(cbrt (pow (log base) 6))
23.0ms	(pow (log base) 6)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: 3 (445.0ms)

Iter	Nodes	Cost
0	175	1950
1	412	1851
2	1202	1690
3	4683	1651
done	5000	1651

prune261.0ms

Filtered

68 candidates to 92 candidates (-35.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	4	12	16
Picked	0	1	1
Done	0	0	0
Total	91	18	109

Merged error: 6.9b

Counts

109 → 18

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
0.7b	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `sqrt-prod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `sqrt-div` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow1/3` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `flip-+` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* (log base) (log base))
2.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
6.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
5.0ms	(sqrt (+ (* re re) (* im im)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (log base) (log base))
23.0ms	(cbrt (pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3))
59.0ms	(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify387.0ms

Counts

102 → 102

Iterations

Useful iterations: done (384.0ms)

Iter	Nodes	Cost
0	151	1396
1	344	1209
2	1172	1024
done	5001	1010

prune151.0ms

Filtered

70 candidates to 102 candidates (-45.7%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	98	22	120

Merged error: 6.9b

Counts

120 → 22

regimes701.0ms

Accuracy

57.4% (10.6b remaining)

Error of 17.8b against oracle of 7.2b and baseline of 32.2b

bsearch167.0ms

Steps

Iters	Range		Point
5	1.8171784245322648e+37	6.43616546702885e+37	3.3662626745557016e+37
9	2.361294668607769e-213	1.9980346609717805e-204	1.0126300995154855e-212
7	-2.410271475432134e-307	2.8466800401792686e-308	-2.8820882891916374e-308
6	-1.1149114536052807e+61	-7.527714714268046e+59	-2.0752208244632336e+60

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	123
1	61	123
done	61	123

end0.0ms

sample2.3s

Algorithm

intervals

Results

833.0ms	8000×	body	80	valid
768.0ms	7896×	body	80	nan

Details

sample76.0ms

simplify6.0ms

prune9.0ms

localize20.0ms

rewrite32.0ms

series80.0ms

simplify466.0ms

prune274.0ms

localize28.0ms

rewrite49.0ms

series80.0ms

simplify809.0ms

prune409.0ms

localize22.0ms

rewrite25.0ms

series76.0ms

simplify1.5s

prune261.0ms

localize23.0ms

rewrite20.0ms

series105.0ms

simplify387.0ms

prune151.0ms

regimes701.0ms

bsearch167.0ms

simplify5.0ms

end0.0ms

sample2.3s

Profiling