Details

sample499.0ms

Algorithm

intervals

Results

165.0ms	89×	body	2560	valid
142.0ms	112×	body	1280	valid
128.0ms	63×	body	10240	exit
26.0ms	37×	body	640	valid
12.0ms	319×	pre	80	true
4.0ms	8×	body	320	valid
1.0ms	8×	body	80	valid
1.0ms	2×	body	160	valid

simplify871.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	2001
4	694
3	215
2	98
1	43
0	17

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 60.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.2b	(- (exp (* a eps)) 1)
2.8b	(- (exp (* b eps)) 1)
4.5b	(- (exp (* (+ a b) eps)) 1)

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

112.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
22.0ms	(- (exp (* a eps)) 1)
29.0ms	(- (exp (* b eps)) 1)
24.0ms	(- (exp (* (+ a b) eps)) 1)

series230.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
47.0ms	(- (exp (* a eps)) 1)
56.0ms	(- (exp (* b eps)) 1)
60.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	2001
3	2001
2	1367
1	395
0	154

prune684.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 50.1b

localize95.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
4.5b	(- (exp (* (+ a b) eps)) 1)
13.8b	(* (* eps eps) (* a a))
14.2b	(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
82×	`add-cbrt-cube` `add-exp-log`
56×	`pow-prod-down`
54×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `associate-/r/`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`frac-times` `cbrt-undiv` `pow-plus` `div-exp` `associate-*r/` `pow-prod-up` `add-cube-cbrt` `insert-posit16`
3×	`flip3-+` `flip-+`
2×	`pow2` `associate-r` `associate-l` `associate-l/` `pow-sqr` `-commutative` `difference-of-squares` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `difference-of-sqr-1` `div-inv` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

306.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
25.0ms	(- (exp (* (+ a b) eps)) 1)
38.0ms	(* (* eps eps) (* a a))
191.0ms	(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

series1.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
76.0ms	(- (exp (* (+ a b) eps)) 1)
59.0ms	(* (* eps eps) (* a a))
113.0ms	(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	2003
2	2003
1	795
0	254

prune745.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 a) (/ 1 b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16`

Counts

1 → 20

Calls

1 calls:

10.0ms

(+ (/ 1 a) (/ 1 b))

series21.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(+ (/ 1 a) (/ 1 b))

simplify1.2s

Counts

23 → 23

Iterations

Iter	Nodes
done	2012
5	2012
4	1333
3	593
2	278
1	105
0	41

prune75.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes176.0ms

Accuracy

85.4% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 3.2b

bsearch4.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	38
1	38
0	26

end0.0ms

sample19.3s

Algorithm

intervals

Results

6.2s	2652×	body	2560	valid
5.7s	3360×	body	1280	valid
4.7s	1886×	body	10240	exit
1.0s	1054×	body	640	valid
866.0ms	9889×	pre	80	true
248.0ms	368×	body	320	valid
77.0ms	427×	body	80	valid
54.0ms	142×	body	160	valid