Details

sample44.0ms

Algorithm

intervals

Results

19.0ms	86×	body	1280	valid
6.0ms	42×	body	640	valid
6.0ms	172×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	16×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.5b	(- (exp (* a x)) 1)

rewrite20.0ms

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))
16.0ms	(- (exp (* a x)) 1)

series66.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
42.0ms	(- (exp (* a x)) 1)

simplify3.0s

Counts

34 → 34

Iterations

Iter	Nodes
done	5002
4	3726
3	1134
2	328
1	123
0	56

prune154.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
3.2b	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
12.6b	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

rewrite622.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `insert-posit16`
2×	`pow2` `+-commutative` `flip3-+` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`associate-+r+`

Counts

4 → 96

Calls

4 calls:

39.0ms	(* (* a x) (* a x))
24.0ms	(* (* a x) (* a x))
101.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
456.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* a x) (* a x))
33.0ms	(* (* a x) (* a x))
90.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
120.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5024
2	1414
1	297
0	95

prune303.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(* (+ (sqrt (exp (* a x))) 1) (- (sqrt (exp (* a x))) 1))
3.5b	(- (sqrt (exp (* a x))) 1)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
11×	`associate-r`
10×	`add-log-exp`
9×	`sqrt-prod`
8×	`difference-of-squares`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-l`
4×	`frac-times` `flip3--` `difference-of-sqr-1` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `exp-prod` `distribute-lft-in` `exp-to-pow` `associate-l/` `associate-r/` `distribute-lft-out` `rem-exp-log`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

4.0ms	(exp (* a x))
5.0ms	(exp (* a x))
68.0ms	(* (+ (sqrt (exp (* a x))) 1) (- (sqrt (exp (* a x))) 1))
14.0ms	(- (sqrt (exp (* a x))) 1)

series195.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (* a x))
22.0ms	(exp (* a x))
93.0ms	(* (+ (sqrt (exp (* a x))) 1) (- (sqrt (exp (* a x))) 1))
64.0ms	(- (sqrt (exp (* a x))) 1)

simplify3.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5184
3	4767
2	1371
1	317
0	113

prune412.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* 1/48 a) (* (* x a) (* x a)))
3.2b	(+ (* 1/2 (* x a)) (* (* 1/8 (* x a)) (* x a)))
4.3b	(* (* (* 1/48 a) (* (* x a) (* x a))) x)
12.6b	(+ (+ (* 1/2 (* x a)) (* (* 1/8 (* x a)) (* x a))) (* (* (* 1/48 a) (* (* x a) (* x a))) x))

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

98×	`pow1` `add-cbrt-cube` `add-exp-log`
73×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`sum-log` `associate-r` `insert-posit16`
2×	`+-commutative` `flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`associate-+l+` `distribute-rgt-out`

Counts

4 → 114

Calls

4 calls:

126.0ms	(* (* 1/48 a) (* (* x a) (* x a)))
32.0ms	(+ (* 1/2 (* x a)) (* (* 1/8 (* x a)) (* x a)))
289.0ms	(* (* (* 1/48 a) (* (* x a) (* x a))) x)
126.0ms	(+ (+ (* 1/2 (* x a)) (* (* 1/8 (* x a)) (* x a))) (* (* (* 1/48 a) (* (* x a) (* x a))) x))

series410.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* 1/48 a) (* (* x a) (* x a)))
104.0ms	(+ (* 1/2 (* x a)) (* (* 1/8 (* x a)) (* x a)))
100.0ms	(* (* (* 1/48 a) (* (* x a) (* x a))) x)
135.0ms	(+ (+ (* 1/2 (* x a)) (* (* 1/8 (* x a)) (* x a))) (* (* (* 1/48 a) (* (* x a) (* x a))) x))

simplify2.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	2406
1	527
0	170

prune413.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes415.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.0b

bsearch2.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	56
1	56
0	36

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	2731×	body	1280	valid
644.0ms	5435×	body	80	valid
256.0ms	1336×	body	640	valid
110.0ms	787×	body	320	valid
32.0ms	368×	body	160	valid