Details

sample76.0ms

Algorithm

intervals

Results

37.0ms	91×	body	1280	valid
12.0ms	154×	body	80	valid
10.0ms	39×	body	640	valid
5.0ms	30×	body	320	valid
1.0ms	11×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2061
8	2061
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.0b	(- (exp (* a x)) 1)

rewrite15.0ms

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:

4.0ms	(exp (* a x))
11.0ms	(- (exp (* a x)) 1)

series71.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
57.0ms	(- (exp (* a x)) 1)

simplify909.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	2009
4	2009
3	1134
2	328
1	123
0	56

prune108.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (* (* a x) (* a x)) a)
4.0b	(* (* 1/6 x) (* (* (* a x) (* a x)) a))
4.4b	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
10.1b	(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

rewrite645.0ms

Algorithm

rewrite-expression-head

Rules

78×	`pow1` `add-cbrt-cube` `add-exp-log`
57×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`sum-log` `associate-r` `insert-posit16`
2×	`+-commutative` `flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`associate-+r+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

68.0ms	(* (* (* a x) (* a x)) a)
181.0ms	(* (* 1/6 x) (* (* (* a x) (* a x)) a))
65.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
327.0ms	(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* (* a x) (* a x)) a)
83.0ms	(* (* 1/6 x) (* (* (* a x) (* a x)) a))
94.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
119.0ms	(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

simplify1.0s

Counts

114 → 114

Iterations

Iter	Nodes
done	2005
2	2005
1	515
0	155

prune235.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (* a x)) (+ 1 (exp (* a x))))
0.0b	(exp (* x (* 3 a)))
0.1b	(* x (* 3 a))
3.9b	(+ -1 (exp (* x (* 3 a))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `*-un-lft-identity` `add-cbrt-cube`
10×	`add-exp-log`
9×	`add-sqr-sqrt`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
5×	`associate-r`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`flip3-+` `associate-r/` `-commutative` `flip-+` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `exp-prod` `sum-log` `distribute-lft-in` `exp-to-pow` `unswap-sqr` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

26.0ms	(* (exp (* a x)) (+ 1 (exp (* a x))))
8.0ms	(exp (* x (* 3 a)))
20.0ms	(* x (* 3 a))
18.0ms	(+ -1 (exp (* x (* 3 a))))

series132.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (exp (* a x)) (+ 1 (exp (* a x))))
20.0ms	(exp (* x (* 3 a)))
22.0ms	(* x (* 3 a))
53.0ms	(+ -1 (exp (* x (* 3 a))))

simplify1.0s

Counts

79 → 79

Iterations

Iter	Nodes
done	2001
3	2001
2	1194
1	337
0	127

prune415.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (exp (* a x))) (cbrt (exp (* a x))))
0.0b	(exp (* x (* 3 a)))
0.1b	(* x (* 3 a))
3.9b	(+ -1 (exp (* x (* 3 a))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`cbrt-prod` `pow1`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`add-exp-log`
9×	`add-cbrt-cube` `associate-l`
8×	`add-log-exp`
7×	`associate-r`
6×	`pow1/3` `swap-sqr`
5×	`pow-prod-down`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `+-commutative` `exp-prod` `sum-log` `flip3-+` `pow-plus` `exp-to-pow` `flip-+` `distribute-lft-out` `rem-exp-log`

Counts

4 → 84

Calls

4 calls:

26.0ms	(* (cbrt (exp (* a x))) (cbrt (exp (* a x))))
8.0ms	(exp (* x (* 3 a)))
16.0ms	(* x (* 3 a))
16.0ms	(+ -1 (exp (* x (* 3 a))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (cbrt (exp (* a x))) (cbrt (exp (* a x))))
24.0ms	(exp (* x (* 3 a)))
26.0ms	(* x (* 3 a))
72.0ms	(+ -1 (exp (* x (* 3 a))))

simplify1.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	2029
3	2029
2	1015
1	328
0	134

prune488.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes239.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch2.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	46
1	46
0	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2698×	body	1280	valid
433.0ms	5338×	body	80	valid
361.0ms	1344×	body	640	valid
157.0ms	740×	body	320	valid
47.0ms	427×	body	160	valid