Details

sample445.0ms

Algorithm

intervals

Results

143.0ms	69×	body	10240	exit
130.0ms	118×	body	1280	valid
115.0ms	75×	body	2560	valid
19.0ms	29×	body	640	valid
12.0ms	325×	pre	80	true
6.0ms	15×	body	320	valid
2.0ms	17×	body	80	valid
0.0ms	2×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
5	4055
4	686
3	213
2	96
1	41
0	17

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.7b	(- (exp (* a eps)) 1)
3.6b	(- (exp (* b eps)) 1)
5.7b	(- (exp (* (+ a b) eps)) 1)

rewrite135.0ms

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:

93.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
16.0ms	(- (exp (* a eps)) 1)
12.0ms	(- (exp (* b eps)) 1)
13.0ms	(- (exp (* (+ a b) eps)) 1)

series180.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
35.0ms	(- (exp (* a eps)) 1)
34.0ms	(- (exp (* b eps)) 1)
53.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
3	4200
2	1288
1	376
0	154

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.0b

localize74.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (+ (* eps (+ (* 1/6 (* (* (* eps a) (* eps a)) a)) (* (* a 1/2) (* eps a)))) (* eps a)) (- (exp (* b eps)) 1))
3.6b	(- (exp (* b eps)) 1)
4.1b	(+ (* 1/6 (* (* (* eps a) (* eps a)) a)) (* (* a 1/2) (* eps a)))
5.7b	(- (exp (* (+ a b) eps)) 1)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

1.0s	(* (+ (* eps (+ (* 1/6 (* (* (* eps a) (* eps a)) a)) (* (* a 1/2) (* eps a)))) (* eps a)) (- (exp (* b eps)) 1))
12.0ms	(- (exp (* b eps)) 1)
223.0ms	(+ (* 1/6 (* (* (* eps a) (* eps a)) a)) (* (* a 1/2) (* eps a)))
19.0ms	(- (exp (* (+ a b) eps)) 1)

series390.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (+ (* eps (+ (* 1/6 (* (* (* eps a) (* eps a)) a)) (* (* a 1/2) (* eps a)))) (* eps a)) (- (exp (* b eps)) 1))
33.0ms	(- (exp (* b eps)) 1)
167.0ms	(+ (* 1/6 (* (* (* eps a) (* eps a)) a)) (* (* a 1/2) (* eps a)))
54.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.2s

Counts

94 → 94

Iterations

Iter	Nodes
2	2614
1	553
0	184

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 44.9b

localize117.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (* (+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2)) eps) (- (exp (* b eps)) 1))
3.6b	(- (exp (* b eps)) 1)
4.1b	(+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2))
5.7b	(- (exp (* (+ a b) eps)) 1)

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

200.0ms	(* (* (+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2)) eps) (- (exp (* b eps)) 1))
12.0ms	(- (exp (* b eps)) 1)
37.0ms	(+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2))
27.0ms	(- (exp (* (+ a b) eps)) 1)

series403.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (* (+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2)) eps) (- (exp (* b eps)) 1))
33.0ms	(- (exp (* b eps)) 1)
117.0ms	(+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2))
74.0ms	(- (exp (* (+ a b) eps)) 1)

simplify939.0ms

Counts

95 → 95

Iterations

Iter	Nodes
2	2337
1	535
0	184

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 44.9b

localize139.0ms

Local error

Found 4 expressions with local error:

4.1b	(+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2))
5.7b	(- (exp (* (+ a b) eps)) 1)
5.7b	(- (exp (* (+ a b) eps)) 1)
5.7b	(- (exp (* (+ a b) eps)) 1)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-log-exp`
13×	`*-un-lft-identity`
6×	`difference-of-squares`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sum-log` `sub-neg` `flip3--` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 65

Calls

4 calls:

49.0ms	(+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2))
25.0ms	(- (exp (* (+ a b) eps)) 1)
26.0ms	(- (exp (* (+ a b) eps)) 1)
25.0ms	(- (exp (* (+ a b) eps)) 1)

series297.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (+ a (* (* 1/6 (* eps a)) (* (* eps a) a))) (* (* (* eps a) a) 1/2))
71.0ms	(- (exp (* (+ a b) eps)) 1)
63.0ms	(- (exp (* (+ a b) eps)) 1)
49.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.3s

Counts

77 → 77

Iterations

Iter	Nodes
3	5246
2	873
1	231
0	89

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 44.9b

regimes307.0ms

Accuracy

41.7% (5.3b remaining)

Error of 51.3b against oracle of 46.0b and baseline of 55.1b

bsearch920.0ms

Steps

Iters	Range		Point
10	4.782460372015072e+141	3.583595561977032e+152	7.448916943974044e+141
9	-150.78695378787688	-0.0006858147917088189	-0.020571153449468284

simplify20.0ms

Iterations

Iter	Nodes
2	66
1	66
0	44

end0.0ms

sample19.7s

Algorithm

intervals

Results

6.6s	2525×	body	2560	valid
6.2s	3462×	body	1280	valid
4.5s	2008×	body	10240	exit
974.0ms	1099×	body	640	valid
555.0ms	10011×	pre	80	true
287.0ms	342×	body	320	valid
104.0ms	450×	body	80	valid
46.0ms	125×	body	160	valid