Details

sample90.0ms

Algorithm

intervals

Results

34.0ms	78×	body	1280	valid
24.0ms	45×	body	640	valid
11.0ms	170×	body	80	valid
5.0ms	24×	body	320	valid
1.0ms	6×	body	160	valid

simplify5.9s

Counts

1 → 1

Iterations

Iter	Nodes
8	6784
7	1297
6	376
5	135
4	56
3	29
2	19
1	14
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
2.2b	(- (exp (* a x)) 1)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

7.0ms	(exp (* a x))
11.0ms	(- (exp (* a x)) 1)

series81.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(exp (* a x))
58.0ms	(- (exp (* a x)) 1)

simplify1.3s

Counts

34 → 34

Iterations

Iter	Nodes
4	3037
3	891
2	297
1	117
0	56

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* a x) (* a x)) (* a x))
0.2b	(* (* a x) (* a x))
0.2b	(* (* 1/2 (* a x)) (* a x))
14.6b	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (* (* (* a x) (* a x)) (* a x)) 1/6)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

219×	`pow1`
101×	`pow-prod-down`
78×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
38×	`pow-prod-up`
19×	`pow-plus`
16×	`pow-sqr`
9×	`add-log-exp`
4×	`pow2` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16`
3×	`sum-log` `associate-r` `associate-l` `*-commutative`
1×	`+-commutative` `associate-+r+` `flip3-+` `swap-sqr` `pow3` `flip-+`

Counts

4 → 153

Calls

4 calls:

102.0ms	(* (* (* a x) (* a x)) (* a x))
44.0ms	(* (* a x) (* a x))
53.0ms	(* (* 1/2 (* a x)) (* a x))
72.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (* (* (* a x) (* a x)) (* a x)) 1/6)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (* (* a x) (* a x)) (* a x))
42.0ms	(* (* a x) (* a x))
50.0ms	(* (* 1/2 (* a x)) (* a x))
133.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (* (* (* a x) (* a x)) (* a x)) 1/6)))

simplify8.1s

Counts

165 → 165

Iterations

Iter	Nodes
3	13023
2	1590
1	414
0	140

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 1/2 (* a x)) (* a x))
0.2b	(* (* a x) (* a x))
1.8b	(log (exp (* (* (* a x) (* a x)) (* a x))))
14.6b	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

65×	`pow1`
37×	`add-cbrt-cube` `add-exp-log`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
10×	`add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`log-prod` `sum-log` `log-pow`
2×	`pow-plus` `associate-r` `associate-l` `*-commutative`
1×	`pow2` `+-commutative` `associate-+r+` `exp-prod` `flip3-+` `exp-to-pow` `swap-sqr` `rem-log-exp` `flip-+`

Counts

4 → 93

Calls

4 calls:

58.0ms	(* (* 1/2 (* a x)) (* a x))
39.0ms	(* (* a x) (* a x))
12.0ms	(log (exp (* (* (* a x) (* a x)) (* a x))))
98.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* 1/2 (* a x)) (* a x))
53.0ms	(* (* a x) (* a x))
79.0ms	(log (exp (* (* (* a x) (* a x)) (* a x))))
143.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))

simplify7.0s

Counts

105 → 105

Iterations

Iter	Nodes
3	12324
2	1439
1	348
0	128

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6))))
14.6b	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))
14.6b	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))
14.6b	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
9×	`sum-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`cbrt-prod` `+-commutative` `associate-+r+`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 56

Calls

4 calls:

62.0ms	(cbrt (+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6))))
107.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))
94.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))
55.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))

series729.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt (+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6))))
147.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))
132.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))
125.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (+ (* a x) (* (log (exp (* (* (* a x) (* a x)) (* a x)))) 1/6)))

simplify6.1s

Counts

68 → 68

Iterations

Iter	Nodes
3	9201
2	1200
1	311
0	115

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes342.0ms

Accuracy

98.4% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.9b

bsearch58.0ms

Steps

Iters	Range		Point
9	-0.018554263322820154	-1.244330994798911e-10	-0.0001298270966635136

simplify7.0ms

Iterations

Iter	Nodes
2	41
1	41
0	28

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2758×	body	1280	valid
431.0ms	1246×	body	640	valid
360.0ms	5535×	body	80	valid
148.0ms	689×	body	320	valid
50.0ms	401×	body	160	valid