Details

sample927.0ms

Algorithm

intervals

Results

412.0ms	304×	pre	80	true
177.0ms	80×	body	2560	valid
149.0ms	95×	body	1280	valid
111.0ms	48×	body	10240	exit
37.0ms	45×	body	640	valid
6.0ms	9×	body	320	valid
4.0ms	22×	body	80	valid
2.0ms	5×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 56.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
3.2b	(- (exp (* b eps)) 1)
3.4b	(- (exp (* a eps)) 1)
5.2b	(- (exp (* (+ a b) eps)) 1)

rewrite141.0ms

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:

84.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
15.0ms	(- (exp (* b eps)) 1)
14.0ms	(- (exp (* a eps)) 1)
27.0ms	(- (exp (* (+ a b) eps)) 1)

series191.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
38.0ms	(- (exp (* b eps)) 1)
38.0ms	(- (exp (* a eps)) 1)
54.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	1348
1	395
0	154

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.8b

localize81.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* eps b) (* (* 1/6 (* (* b b) b)) (* eps (* eps eps)))) (* (* (* eps b) (* eps b)) 1/2))))
3.4b	(- (exp (* a eps)) 1)
5.2b	(- (exp (* (+ a b) eps)) 1)
16.9b	(* (* 1/6 (* (* b b) b)) (* eps (* eps eps)))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-cbrt-cube` `add-exp-log`
58×	`pow1`
46×	`prod-exp` `cbrt-unprod`
42×	`pow-prod-down`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `difference-of-sqr-1` `associate-*l/` `distribute-lft-out--` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-r` `associate-l` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 113

Calls

4 calls:

136.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* eps b) (* (* 1/6 (* (* b b) b)) (* eps (* eps eps)))) (* (* (* eps b) (* eps b)) 1/2))))
11.0ms	(- (exp (* a eps)) 1)
15.0ms	(- (exp (* (+ a b) eps)) 1)
174.0ms	(* (* 1/6 (* (* b b) b)) (* eps (* eps eps)))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.7s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* eps b) (* (* 1/6 (* (* b b) b)) (* eps (* eps eps)))) (* (* (* eps b) (* eps b)) 1/2))))
40.0ms	(- (exp (* a eps)) 1)
83.0ms	(- (exp (* (+ a b) eps)) 1)
111.0ms	(* (* 1/6 (* (* b b) b)) (* eps (* eps eps)))

simplify1.4s

Counts

125 → 125

Iterations

Iter	Nodes
done	2002
2	2002
1	820
0	257

prune2.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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:

19.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify1.3s

Counts

23 → 23

Iterations

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

prune224.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize142.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (exp (* (+ a b) eps)) 1)
5.3b	(* b (* eps (* eps eps)))
11.6b	(* (* b b) (* b (* eps (* eps eps))))
13.9b	(/ (- (exp (* (+ a b) eps)) 1) (+ (+ (* (* (* b b) (* b (* eps (* eps eps)))) 1/6) (* eps b)) (* (* eps b) (* (* eps b) 1/2))))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

47×	`add-cbrt-cube` `add-exp-log`
45×	`pow1`
37×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`pow-prod-down` `prod-exp` `cbrt-unprod`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`associate-l` `insert-posit16`
3×	`associate-/r*`
2×	`flip3--` `associate-r` `associate-/r/` `*-commutative` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 123

Calls

4 calls:

24.0ms	(- (exp (* (+ a b) eps)) 1)
35.0ms	(* b (* eps (* eps eps)))
147.0ms	(* (* b b) (* b (* eps (* eps eps))))
2.8s	(/ (- (exp (* (+ a b) eps)) 1) (+ (+ (* (* (* b b) (* b (* eps (* eps eps)))) 1/6) (* eps b)) (* (* eps b) (* (* eps b) 1/2))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (exp (* (+ a b) eps)) 1)
49.0ms	(* b (* eps (* eps eps)))
94.0ms	(* (* b b) (* b (* eps (* eps eps))))
303.0ms	(/ (- (exp (* (+ a b) eps)) 1) (+ (+ (* (* (* b b) (* b (* eps (* eps eps)))) 1/6) (* eps b)) (* (* eps b) (* (* eps b) 1/2))))

simplify1.0s

Counts

135 → 135

Iterations

Iter	Nodes
done	2000
2	2000
1	569
0	214

prune2.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

0% (3.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample19.5s

Algorithm

intervals

Results

6.6s	2494×	body	2560	valid
5.3s	3464×	body	1280	valid
4.7s	1940×	body	10240	exit
1.1s	1131×	body	640	valid
1.0s	9942×	pre	80	true
272.0ms	342×	body	320	valid
76.0ms	426×	body	80	valid
55.0ms	145×	body	160	valid