Details

sample103.0ms

Algorithm

intervals

Results

53.0ms	66×	body	10240	exit
21.0ms	263×	body	80	valid
3.0ms	6×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	2×	body	1280	valid
1.0ms	6×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize59.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

24.0ms	(+ 1.0 (exp x))
50.0ms	(- (log (+ 1.0 (exp x))) (* x y))
19.0ms	(log (+ 1.0 (exp x)))

series287.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1.0 (exp x))
129.0ms	(- (log (+ 1.0 (exp x))) (* x y))
139.0ms	(log (+ 1.0 (exp x)))

simplify8.0s

Counts

57 → 57

Iterations

Iter	Nodes
done	5011
4	4738
3	1557
2	532
1	214
0	95

prune607.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize150.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (cbrt (log (+ 1.0 (exp x)))) (cbrt (log (+ 1.0 (exp x))))) (cbrt (log (+ 1.0 (exp x)))))
1.1b	(cbrt (log (+ 1.0 (exp x))))
1.1b	(cbrt (log (+ 1.0 (exp x))))
1.1b	(cbrt (log (+ 1.0 (exp x))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
17×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
7×	`associate-r`
6×	`pow-plus`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`log-pow` `insert-posit16` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 76

Calls

4 calls:

90.0ms	(* (* (cbrt (log (+ 1.0 (exp x)))) (cbrt (log (+ 1.0 (exp x))))) (cbrt (log (+ 1.0 (exp x)))))
5.0ms	(cbrt (log (+ 1.0 (exp x))))
6.0ms	(cbrt (log (+ 1.0 (exp x))))
4.0ms	(cbrt (log (+ 1.0 (exp x))))

series1.7s

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (* (cbrt (log (+ 1.0 (exp x)))) (cbrt (log (+ 1.0 (exp x))))) (cbrt (log (+ 1.0 (exp x)))))
492.0ms	(cbrt (log (+ 1.0 (exp x))))
492.0ms	(cbrt (log (+ 1.0 (exp x))))
524.0ms	(cbrt (log (+ 1.0 (exp x))))

simplify5.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	2093
2	692
1	236
0	96

prune822.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize108.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* x x) 1/2)
0.0b	(+ (+ 2.0 x) (* (* x x) 1/2))
0.0b	(- (log (+ (+ 2.0 x) (* (* x x) 1/2))) (* x y))
7.5b	(log (+ (+ 2.0 x) (* (* x x) 1/2)))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-log-exp`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`log-prod`
4×	`log-div` `insert-posit16`
3×	`sum-log` `flip3-+` `associate-r` `pow-prod-down` `prod-exp` `associate--l+` `cbrt-unprod` `flip-+`
2×	`associate--l-`
1×	`+-commutative` `associate-+l+` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `associate-l` `log-pow` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

77.0ms	(* (* x x) 1/2)
91.0ms	(+ (+ 2.0 x) (* (* x x) 1/2))
78.0ms	(- (log (+ (+ 2.0 x) (* (* x x) 1/2))) (* x y))
56.0ms	(log (+ (+ 2.0 x) (* (* x x) 1/2)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* x x) 1/2)
24.0ms	(+ (+ 2.0 x) (* (* x x) 1/2))
155.0ms	(- (log (+ (+ 2.0 x) (* (* x x) 1/2))) (* x y))
92.0ms	(log (+ (+ 2.0 x) (* (* x x) 1/2)))

simplify8.9s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4732
2	1159
1	372
0	145

prune884.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize173.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 x) (* 0.25 (* x x)))
0.0b	(- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0)))
0.0b	(- (+ (+ (* 0.5 x) (* 0.25 (* x x))) (- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0)))) (* x y))
6.2b	(+ (+ (* 0.5 x) (* 0.25 (* x x))) (- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0))))

rewrite734.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-log-exp`
13×	`sum-log`
10×	`diff-log`
8×	`*-un-lft-identity`
7×	`associate--l+`
6×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt`
5×	`associate-+r+`
4×	`pow1` `flip3-+` `flip3--` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `flip--`
3×	`sub-neg`
2×	`+-commutative` `associate-+r-`
1×	`associate--l-` `associate-+l+` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

19.0ms	(+ (* 0.5 x) (* 0.25 (* x x)))
24.0ms	(- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0)))
581.0ms	(- (+ (+ (* 0.5 x) (* 0.25 (* x x))) (- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0)))) (* x y))
107.0ms	(+ (+ (* 0.5 x) (* 0.25 (* x x))) (- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0))))

series693.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (* 0.5 x) (* 0.25 (* x x)))
456.0ms	(- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0)))
75.0ms	(- (+ (+ (* 0.5 x) (* 0.25 (* x x))) (- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0)))) (* x y))
48.0ms	(+ (+ (* 0.5 x) (* 0.25 (* x x))) (- (log 2.0) (* (* 1/2 (/ x 2.0)) (/ x 2.0))))

simplify4.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5004
2	2088
1	492
0	149

prune752.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes327.0ms

Accuracy

58.7% (0.5b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 1.5b

bsearch148.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	32.81305289360078	9.261101280752574e-07
6	-252269475.2976281	-15918868.771886915	-16179825.06434172

simplify18.0ms

Iterations

Iter	Nodes
done	44
1	44
0	32

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.0s	2386×	body	10240	exit
1.0s	8495×	body	80	valid
115.0ms	258×	body	640	valid
82.0ms	107×	body	1280	valid
55.0ms	202×	body	320	valid
16.0ms	90×	body	160	valid