Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

273×

body

valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	21	11
2	36	11
3	57	11
4	85	11
5	106	11
done	106	11

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: 6.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.2b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b	(* y (+ 1.0 (* z z)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 70

Calls

2 calls:

9.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
6.0ms	(* y (+ 1.0 (* z z)))

series30.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
11.0ms	(* y (+ 1.0 (* z z)))

simplify643.0ms

Counts

76 → 76

Iterations

Useful iterations: done (641.0ms)

Iter	Nodes	Cost
0	156	1062
1	410	1041
2	1532	901
done	5000	887

prune137.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 4.7b

Counts

77 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.2b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
18.2b	(sqrt (+ 1.0 (* z z)))
18.2b	(sqrt (+ 1.0 (* z z)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
8×	`frac-times` `associate-/r/`
6×	`associate-r`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

12.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
22.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
3.0ms	(sqrt (+ 1.0 (* z z)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
19.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
4.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

simplify713.0ms

Counts

129 → 129

Iterations

Useful iterations: done (709.0ms)

Iter	Nodes	Cost
0	217	2776
1	610	2149
2	2588	1834
done	5001	1748

prune235.0ms

Filtered

96 candidates to 129 candidates (-34.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	130	6	136

Merged error: 4.7b

Counts

136 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.3b	(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* y (sqrt (+ 1.0 (* z z)))))
18.2b	(sqrt (+ 1.0 (* z z)))
18.2b	(sqrt (+ (* z z) 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
29×	`add-cbrt-cube`
18×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`times-frac`
6×	`pow1` `sqrt-div` `sqrt-prod`
5×	`associate-/l*`
4×	`add-log-exp`
3×	`cbrt-prod` `flip3-+` `flip-+` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `associate-/r/`
1×	`frac-2neg` `pow1/3` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 85

Calls

4 calls:

1.0ms	(cbrt x)
16.0ms	(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* y (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
5.0ms	(sqrt (+ (* z z) 1.0))

series115.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt x)
69.0ms	(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* y (sqrt (+ 1.0 (* z z)))))
4.0ms	(sqrt (+ 1.0 (* z z)))
11.0ms	(sqrt (+ (* z z) 1.0))

simplify681.0ms

Counts

97 → 97

Iterations

Useful iterations: done (678.0ms)

Iter	Nodes	Cost
0	235	1923
1	632	1707
2	2803	1391
done	5000	1374

prune264.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Merged error: 4.7b

Counts

103 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (sqrt 1.0) (* (sqrt (+ (* z z) 1.0)) x))
1.1b	(* (/ (sqrt 1.0) (* y (sqrt (+ 1.0 (* z z))))) (/ (sqrt 1.0) (* (sqrt (+ (* z z) 1.0)) x)))
18.2b	(sqrt (+ 1.0 (* z z)))
18.2b	(sqrt (+ (* z z) 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

11.0ms	(/ (sqrt 1.0) (* (sqrt (+ (* z z) 1.0)) x))
21.0ms	(* (/ (sqrt 1.0) (* y (sqrt (+ 1.0 (* z z))))) (/ (sqrt 1.0) (* (sqrt (+ (* z z) 1.0)) x)))
3.0ms	(sqrt (+ 1.0 (* z z)))
5.0ms	(sqrt (+ (* z z) 1.0))

series54.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (sqrt 1.0) (* (sqrt (+ (* z z) 1.0)) x))
29.0ms	(* (/ (sqrt 1.0) (* y (sqrt (+ 1.0 (* z z))))) (/ (sqrt 1.0) (* (sqrt (+ (* z z) 1.0)) x)))
4.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ (* z z) 1.0))

simplify885.0ms

Counts

126 → 126

Iterations

Useful iterations: done (874.0ms)

Iter	Nodes	Cost
0	242	2825
1	665	2441
2	3205	2110
done	5000	1645

prune251.0ms

Filtered

91 candidates to 126 candidates (-38.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	126	6	132

Merged error: 4.7b

Counts

132 → 6

regimes471.0ms

Accuracy

83.2% (0.2b remaining)

Error of 5.3b against oracle of 5.1b and baseline of 6.3b

bsearch36.0ms

Steps

Iters	Range		Point
8	100.28207043192755	3833461.518986408	17176.799346420077
9	-4.612443093568723e+44	-2.6651291608236074e+37	-1.2219681213183615e+38

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	19	49
1	26	37
done	26	37

end0.0ms

sample724.0ms

Algorithm

intervals

Results

349.0ms

8596×

body

valid

Details

sample25.0ms

simplify48.0ms

prune3.0ms

localize7.0ms

rewrite17.0ms

series30.0ms

simplify643.0ms

prune137.0ms

localize10.0ms

rewrite44.0ms

series38.0ms

simplify713.0ms

prune235.0ms

localize20.0ms

rewrite28.0ms

series115.0ms

simplify681.0ms

prune264.0ms

localize21.0ms

rewrite44.0ms

series54.0ms

simplify885.0ms

prune251.0ms

regimes471.0ms

bsearch36.0ms

simplify2.0ms

end0.0ms

sample724.0ms

Profiling