Details

sample423.0ms

Algorithm

intervals

Results

178.0ms	85×	body	2560	valid
101.0ms	105×	body	1280	valid
84.0ms	54×	body	10240	exit
22.0ms	38×	body	640	valid
12.0ms	310×	pre	80	true
5.0ms	10×	body	320	valid
2.0ms	12×	body	80	valid
1.0ms	6×	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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
3.1b	(- (exp (* a eps)) 1)
3.9b	(- (exp (* b 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:

79.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
23.0ms	(- (exp (* a eps)) 1)
17.0ms	(- (exp (* b eps)) 1)
20.0ms	(- (exp (* (+ a b) eps)) 1)

series164.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
34.0ms	(- (exp (* a eps)) 1)
34.0ms	(- (exp (* b eps)) 1)
46.0ms	(- (exp (* (+ a b) eps)) 1)

simplify924.0ms

Counts

102 → 102

Iterations

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

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 46.8b

localize66.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* 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)))
5.2b	(- (exp (* (+ a b) eps)) 1)
12.6b	(* (* eps eps) (* a a))
15.0b	(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

rewrite384.0ms

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:

178.0ms	(/ (* 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)))
12.0ms	(- (exp (* (+ a b) eps)) 1)
27.0ms	(* (* eps eps) (* a a))
163.0ms	(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

series1.0s

Counts

4 → 12

Calls

4 calls:

840.0ms	(/ (* 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)))
48.0ms	(- (exp (* (+ a b) eps)) 1)
30.0ms	(* (* eps eps) (* a a))
88.0ms	(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

simplify1.2s

Counts

138 → 138

Iterations

Iter	Nodes
done	2003
2	2003
1	795
0	254

prune2.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite29.0ms

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:

29.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(+ (/ 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

prune153.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 163

Calls

4 calls:

70.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
7.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
7.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
10.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
104.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
118.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
125.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

simplify1.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	2003
3	2003
2	1136
1	426
0	180

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes204.0ms

Accuracy

0% (3.1b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 3.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample18.4s

Algorithm

intervals

Results

6.1s	3487×	body	1280	valid
5.5s	2545×	body	2560	valid
4.4s	1929×	body	10240	exit
1.0s	1063×	body	640	valid
526.0ms	9931×	pre	80	true
198.0ms	362×	body	320	valid
128.0ms	411×	body	80	valid
84.0ms	134×	body	160	valid