Details

sample88.0ms

Algorithm

intervals

Results

31.0ms	375×	body	80	valid
24.0ms	361×	body	80	nan

simplify1.2s

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	440	24
5	867	24
6	1680	24
7	4592	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

localize18.0ms

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)

rewrite42.0ms

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)

series135.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
23.0ms	(* (- x 0.5) (log x))
38.0ms	(- (* (- x 0.5) (log x)) x)
29.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify523.0ms

Counts

110 → 110

Iterations

Useful iterations: done (519.0ms)

Iter	Nodes	Cost
0	222	1715
1	544	1631
2	1645	1492
done	5001	1422

prune240.0ms

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

localize24.0ms

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)

rewrite23.0ms

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)
2.0ms	(cbrt x)
17.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series99.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt x)
23.0ms	(cbrt x)
25.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify533.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	105	938
1	232	912
2	595	830
3	1669	778
done	5000	778

prune154.0ms

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

localize22.0ms

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:

10.0ms	(* (- x 0.5) (log (sqrt x)))
10.0ms	(* (- 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)

series52.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (- x 0.5) (log (sqrt x)))
9.0ms	(* (- 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)

simplify495.0ms

Counts

139 → 139

Iterations

Useful iterations: done (487.0ms)

Iter	Nodes	Cost
0	221	2188
1	507	2102
2	1666	1962
done	5002	1900

prune257.0ms

Filtered

99 candidates to 139 candidates (-40.4%)

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

localize26.0ms

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)

rewrite33.0ms

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)
14.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series195.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (- x 0.5) (log (cbrt x))))
27.0ms	(cbrt x)
23.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify531.0ms

Counts

94 → 94

Iterations

Useful iterations: done (528.0ms)

Iter	Nodes	Cost
0	213	1772
1	572	1660
2	1873	1405
done	5000	1393

prune181.0ms

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

regimes555.0ms

Accuracy

89.8% (0.2b remaining)

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

bsearch16.0ms

Steps

Iters	Range		Point
4	7008501314990.282	9624807603436.258	8178286720088.45

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.6s

Algorithm

intervals

Results

871.0ms	11909×	body	80	valid
813.0ms	12057×	body	80	nan

Details

sample88.0ms

simplify1.2s

prune4.0ms

localize18.0ms

rewrite42.0ms

series135.0ms

simplify523.0ms

prune240.0ms

localize24.0ms

rewrite23.0ms

series99.0ms

simplify533.0ms

prune154.0ms

localize22.0ms

rewrite47.0ms

series52.0ms

simplify495.0ms

prune257.0ms

localize26.0ms

rewrite33.0ms

series195.0ms

simplify531.0ms

prune181.0ms

regimes555.0ms

bsearch16.0ms

simplify4.0ms

end0.0ms

sample2.6s

Profiling