Details

sample28.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify787.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	21
1	35	21
2	63	21
3	120	21
4	203	21
5	291	21
6	368	21
7	474	21
8	576	21
9	612	21
10	614	21
done	614	21

prune3.0ms

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: 24.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
23.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-*r/`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

11.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
11.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
16.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series120.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
16.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
26.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.0s

Counts

91 → 91

Iterations

Useful iterations: 2 (185.0ms)

Iter	Nodes	Cost
0	190	1805
1	535	1717
2	1769	1525
done	5000	1525

prune173.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	6	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0.0b

Counts

92 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
18.0b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-*r/` `clear-num` `sum-log`

Counts

4 → 96

Calls

4 calls:

4.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
8.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
20.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
16.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series114.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
26.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify821.0ms

Counts

108 → 108

Iterations

Useful iterations: done (816.0ms)

Iter	Nodes	Cost
0	209	2472
1	556	2382
2	1710	2150
done	5000	2130

prune192.0ms

Filtered

80 candidates to 108 candidates (-35.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	108	6	114

Merged error: 0.0b

Counts

114 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
17.3b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
17.3b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
17.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

35.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
4.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
4.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify957.0ms

Counts

162 → 162

Iterations

Useful iterations: done (948.0ms)

Iter	Nodes	Cost
0	258	4914
1	720	4681
2	2445	4138
done	5000	4088

prune403.0ms

Filtered

118 candidates to 162 candidates (-37.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	162	6	168

Merged error: 0.0b

Counts

168 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

15.2b	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
17.8b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
17.8b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
17.8b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
24×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-prod` `cbrt-div`
18×	`add-cbrt-cube`
15×	`associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 108

Calls

4 calls:

39.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
6.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series52.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
8.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
9.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify997.0ms

Counts

120 → 120

Iterations

Useful iterations: done (990.0ms)

Iter	Nodes	Cost
0	236	4390
1	701	4251
2	2642	3493
done	5000	3477

prune426.0ms

Filtered

103 candidates to 120 candidates (-16.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	120	6	126

Merged error: 0.0b

Counts

126 → 6

regimes260.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 17.1b

bsearch50.0ms

Steps

Iters	Range		Point
10	6.447125064489246e-12	18.076566431700634	17.753460078900254
10	-8.577185052646821e+30	-878796860755045.6	-2.585394428984934e+26

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	51
1	46	41
done	46	41

end0.0ms

sample791.0ms

Algorithm

intervals

Results

476.0ms

8000×

body

valid

Details

sample28.0ms

simplify787.0ms

prune3.0ms

localize14.0ms

rewrite47.0ms

series120.0ms

simplify1.0s

prune173.0ms

localize14.0ms

rewrite50.0ms

series114.0ms

simplify821.0ms

prune192.0ms

localize17.0ms

rewrite74.0ms

series43.0ms

simplify957.0ms

prune403.0ms

localize19.0ms

rewrite68.0ms

series52.0ms

simplify997.0ms

prune426.0ms

regimes260.0ms

bsearch50.0ms

simplify3.0ms

end0.0ms

sample791.0ms

Profiling