Details

sample85.0ms

Algorithm

intervals

Results

35.0ms	76×	body	1280	valid
15.0ms	49×	body	640	valid
12.0ms	162×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify5.9s

Counts

1 → 1

Iterations

Iter	Nodes
8	6498
7	1279
6	374
5	133
4	54
3	27
2	17
1	12
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize17.0ms

Local error

Found 1 expressions with local error:

4.3b	(- (exp (* a x)) 1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

25.0ms

(- (exp (* a x)) 1)

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(- (exp (* a x)) 1)

simplify1.3s

Counts

20 → 20

Iterations

Iter	Nodes
4	2847
3	848
2	269
1	105
0	48

prune219.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize418.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) 1/2)
0.2b	(* (* a x) (* (* a x) 1/2))
0.2b	(* (* a x) (* a x))
10.6b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

69×	`pow1`
42×	`add-cbrt-cube` `add-exp-log`
35×	`pow-prod-down`
26×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`associate-l` `*-commutative`
2×	`pow-plus`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 95

Calls

4 calls:

29.0ms	(* (* a x) 1/2)
89.0ms	(* (* a x) (* (* a x) 1/2))
24.0ms	(* (* a x) (* a x))
285.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* a x) 1/2)
54.0ms	(* (* a x) (* (* a x) 1/2))
40.0ms	(* (* a x) (* a x))
165.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))

simplify11.1s

Counts

107 → 107

Iterations

Iter	Nodes
3	11575
2	1475
1	363
0	117

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
4.0b	(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2))))) (* a x))
4.8b	(log (exp (* (* a x) 1/2)))
11.2b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2)))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log`
12×	`add-log-exp`
9×	`log-prod`
8×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-+r+`
4×	`sum-log` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `log-pow`
2×	`+-commutative` `flip3-+` `pow-plus` `flip-+`
1×	`pow2` `associate-+l+` `exp-prod` `exp-to-pow` `swap-sqr` `rem-log-exp` `associate-r` `associate-l` `*-commutative`

Counts

4 → 82

Calls

4 calls:

29.0ms	(* (* a x) (* a x))
1.7s	(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2))))) (* a x))
7.0ms	(log (exp (* (* a x) 1/2)))
323.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2)))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* a x) (* a x))
552.0ms	(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2))))) (* a x))
33.0ms	(log (exp (* (* a x) 1/2)))
162.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2)))))

simplify9.0s

Counts

94 → 94

Iterations

Iter	Nodes
3	14621
2	1514
1	385
0	130

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
4.0b	(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x)))))) (* a x))
4.8b	(log (sqrt (exp (* a x))))
11.2b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x))))))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
18×	`log-prod`
17×	`pow-prod-down` `add-exp-log`
16×	`add-cbrt-cube`
12×	`associate-+r+` `add-log-exp`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
8×	`prod-exp` `cbrt-unprod`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`log-pow`
4×	`sum-log` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`sqrt-pow1`
2×	`+-commutative` `flip3-+` `pow-plus` `flip-+`
1×	`pow2` `associate-+l+` `exp-prod` `exp-to-pow` `pow1/2` `swap-sqr` `rem-log-exp` `associate-r` `associate-l` `*-commutative`

Counts

4 → 93

Calls

4 calls:

48.0ms	(* (* a x) (* a x))
1.7s	(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x)))))) (* a x))
4.0ms	(log (sqrt (exp (* a x))))
319.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x))))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* a x) (* a x))
286.0ms	(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x)))))) (* a x))
45.0ms	(log (sqrt (exp (* a x))))
213.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x))))))

simplify5.9s

Counts

105 → 105

Iterations

Iter	Nodes
3	10149
2	1492
1	420
0	148

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.7b

bsearch48.0ms

Steps

Iters	Range		Point
8	-0.01568834547608203	-7.965106996193536e-06	-0.00014871104845393037

simplify7.0ms

Iterations

Iter	Nodes
2	26
1	26
0	20

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	2768×	body	1280	valid
484.0ms	5504×	body	80	valid
452.0ms	1344×	body	640	valid
148.0ms	672×	body	320	valid
47.0ms	369×	body	160	valid