Details

sample86.0ms

Algorithm

intervals

Results

31.0ms	375×	body	80	valid
23.0ms	361×	body	80	nan

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	24
1	37	24
2	83	24
3	191	24
4	421	24
5	820	24
6	1498	24
7	3846	24
done	5000	24

prune4.0ms

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: 7.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
8.0ms	(* (- x 0.5) (log x))
8.0ms	(- (* (- x 0.5) (log x)) x)
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series128.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
23.0ms	(* (- x 0.5) (log x))
43.0ms	(- (* (- x 0.5) (log x)) x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify908.0ms

Counts

110 → 110

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	222	1715
1	531	1629
2	1532	1481
done	5000	1419

prune227.0ms

Filtered

85 candidates to 110 candidates (-29.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Merged error: 4.8b

Counts

111 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series98.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
24.0ms	(cbrt x)
27.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify997.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (327.0ms)

Iter	Nodes	Cost
0	105	938
1	231	912
2	564	828
3	1608	778
done	5000	778

prune149.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Merged error: 4.8b

Counts

82 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log (sqrt x)))
0.1b	(* (- x 0.5) (log (sqrt x)))
0.1b	(- (* (- x 0.5) (log (sqrt x))) x)
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `log-prod`
32×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
12×	`pow1` `associate-r` `associate--l+`
10×	`add-exp-log` `associate-l` `add-cbrt-cube`
9×	`times-frac`
6×	`log-pow` `add-log-exp`
4×	`associate-*l/`
3×	`flip3--` `associate-/r` `flip--` `associate-/l`
2×	`sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 127

Calls

4 calls:

13.0ms	(* (- x 0.5) (log (sqrt x)))
9.0ms	(* (- x 0.5) (log (sqrt x)))
9.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series51.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
12.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify706.0ms

Counts

139 → 139

Iterations

Useful iterations: done (701.0ms)

Iter	Nodes	Cost
0	221	2188
1	499	2096
2	1563	1944
done	5000	1900

prune428.0ms

Filtered

98 candidates to 139 candidates (-41.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Merged error: 4.8b

Counts

146 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (- x 0.5) (log (cbrt x))))
0.5b	(cbrt x)
0.5b	(cbrt x)
6.4b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod` `associate-+r+` `log-prod`
9×	`times-frac`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-+l+` `flip3--` `associate-r/` `associate-l/` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 82

Calls

4 calls:

13.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (- x 0.5) (log (cbrt x))))
2.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series192.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (- x 0.5) (log (cbrt x))))
23.0ms	(cbrt x)
27.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify768.0ms

Counts

94 → 94

Iterations

Useful iterations: done (764.0ms)

Iter	Nodes	Cost
0	213	1772
1	571	1658
2	1798	1399
done	5001	1333

prune172.0ms

Filtered

79 candidates to 94 candidates (-19.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	94	7	101

Merged error: 4.8b

Counts

101 → 7

regimes533.0ms

Accuracy

89.7% (0.2b remaining)

Error of 4.3b against oracle of 4.1b and baseline of 6.4b

bsearch35.0ms

Steps

Iters	Range		Point
8	9624807603436.258	1.070528705284242e+17	17216894534051.332

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	77
1	57	77
done	57	77

end0.0ms

sample2.6s

Algorithm

intervals

Results

862.0ms	11909×	body	80	valid
821.0ms	12057×	body	80	nan

Details

sample86.0ms

simplify3.8s

prune4.0ms

localize23.0ms

rewrite43.0ms

series128.0ms

simplify908.0ms

prune227.0ms

localize26.0ms

rewrite18.0ms

series98.0ms

simplify997.0ms

prune149.0ms

localize20.0ms

rewrite47.0ms

series51.0ms

simplify706.0ms

prune428.0ms

localize23.0ms

rewrite31.0ms

series192.0ms

simplify768.0ms

prune172.0ms

regimes533.0ms

bsearch35.0ms

simplify4.0ms

end0.0ms

sample2.6s

Profiling