Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	375×	body	80	valid
25.0ms	361×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	24
1	37	24
2	83	24
3	193	24
4	434	24
5	909	24
6	1646	24
7	4382	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

localize26.0ms

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)

rewrite44.0ms

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)

series144.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
27.0ms	(* (- x 0.5) (log x))
48.0ms	(- (* (- x 0.5) (log x)) x)
25.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify523.0ms

Counts

110 → 110

Iterations

Useful iterations: done (517.0ms)

Iter	Nodes	Cost
0	222	1715
1	544	1629
2	1590	1489
done	5000	1422

prune242.0ms

Filtered

88 candidates to 110 candidates (-25.0%)

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

localize27.0ms

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)

rewrite19.0ms

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)
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series108.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt x)
30.0ms	(cbrt x)
27.0ms	(cbrt x)
25.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify530.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (177.0ms)

Iter	Nodes	Cost
0	105	938
1	232	912
2	594	828
3	1994	778
done	5000	778

prune157.0ms

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

localize23.0ms

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)

rewrite45.0ms

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:

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
15.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
26.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify477.0ms

Counts

139 → 139

Iterations

Useful iterations: done (472.0ms)

Iter	Nodes	Cost
0	221	2188
1	507	2100
2	1604	1944
done	5000	1900

prune262.0ms

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

localize24.0ms

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)

rewrite32.0ms

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)
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series215.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (- x 0.5) (log (cbrt x))))
26.0ms	(cbrt x)
27.0ms	(cbrt x)
28.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify540.0ms

Counts

94 → 94

Iterations

Useful iterations: done (537.0ms)

Iter	Nodes	Cost
0	213	1772
1	572	1660
2	1869	1399
done	5000	1393

prune194.0ms

Filtered

79 candidates to 94 candidates (-19.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Merged error: 4.8b

Counts

101 → 7

regimes592.0ms

Accuracy

89.8% (0.2b remaining)

Error of 4.3b against oracle of 4.1b and baseline of 6.5b

bsearch17.0ms

Steps

Iters	Range		Point
4	7008501314990.282	9624807603436.258	8178286720088.45

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	86
1	63	86
done	63	86

end0.0ms

sample2.7s

Algorithm

intervals

Results

895.0ms	11909×	body	80	valid
827.0ms	12057×	body	80	nan

Details

sample91.0ms

simplify1.3s

prune4.0ms

localize26.0ms

rewrite44.0ms

series144.0ms

simplify523.0ms

prune242.0ms

localize27.0ms

rewrite19.0ms

series108.0ms

simplify530.0ms

prune157.0ms

localize23.0ms

rewrite45.0ms

series61.0ms

simplify477.0ms

prune262.0ms

localize24.0ms

rewrite32.0ms

series215.0ms

simplify540.0ms

prune194.0ms

regimes592.0ms

bsearch17.0ms

simplify5.0ms

end0.0ms

sample2.7s

Profiling