Details

sample342.0ms

Algorithm

intervals

Results

116.0ms	82×	body	2560	valid
73.0ms	113×	body	1280	valid
73.0ms	66×	body	10240	exit
46.0ms	29×	body	640	valid
9.0ms	322×	pre	80	true
3.0ms	13×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	3×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	245	24
4	692	24
5	3301	24
done	5001	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ a b) eps)
2.3b	(- (exp (* b eps)) 1.0)
2.5b	(- (exp (* a eps)) 1.0)
4.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-l`
3×	`sub-neg` `flip3--` `diff-log` `associate-r` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

27.0ms	(* (+ a b) eps)
21.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (+ a b) eps)
38.0ms	(- (exp (* b eps)) 1.0)
41.0ms	(- (exp (* a eps)) 1.0)
74.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.9s

Counts

75 → 75

Iterations

Useful iterations: 3 (853.0ms)

Iter	Nodes	Cost
0	139	782
1	308	762
2	893	682
3	2697	676
done	5000	676

prune398.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 47.3b

localize28.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (* 1/6 (pow a 3)) eps)
4.3b	(- (exp (* (+ a b) eps)) 1.0)
8.3b	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a)))
11.1b	(* (* eps eps) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

24.0ms	(* (* 1/6 (pow a 3)) eps)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
25.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a)))
105.0ms	(* (* eps eps) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* 1/6 (pow a 3)) eps)
86.0ms	(- (exp (* (+ a b) eps)) 1.0)
76.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a)))
154.0ms	(* (* eps eps) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))

simplify1.6s

Counts

79 → 79

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	141	1355
1	389	1257
2	1655	1087
done	5001	1085

prune540.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 47.2b

localize61.0ms

Local error

Found 4 expressions with local error:

4.3b	(- (exp (* (+ a b) eps)) 1.0)
6.0b	(* eps (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))
8.3b	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a)))
11.9b	(cbrt (pow (* eps (* eps (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))) 3))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`cbrt-prod` `add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-*r/` `add-cbrt-cube`
3×	`flip3-+` `associate-r` `associate-l` `flip-+`
2×	`cube-div` `cbrt-div`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `sub-neg` `unpow-prod-down` `flip3--` `distribute-lft-in` `pow1/3` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

24.0ms	(- (exp (* (+ a b) eps)) 1.0)
98.0ms	(* eps (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))
36.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a)))
63.0ms	(cbrt (pow (* eps (* eps (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))) 3))

series561.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (exp (* (+ a b) eps)) 1.0)
165.0ms	(* eps (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))
119.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a)))
197.0ms	(cbrt (pow (* eps (* eps (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (* a a))))) 3))

simplify1.7s

Counts

78 → 78

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	145	1729
1	373	1559
2	1452	1431
done	5001	1419

prune571.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 47.2b

localize45.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps)))) (* eps b)))
4.1b	(* (* 1/6 (pow eps 3)) b)
4.3b	(- (exp (* (+ a b) eps)) 1.0)
14.4b	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps))))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

297.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps)))) (* eps b)))
47.0ms	(* (* 1/6 (pow eps 3)) b)
19.0ms	(- (exp (* (+ a b) eps)) 1.0)
141.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps)))) (* eps b)))
35.0ms	(* (* 1/6 (pow eps 3)) b)
81.0ms	(- (exp (* (+ a b) eps)) 1.0)
136.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps))))

simplify2.5s

Counts

98 → 98

Iterations

Useful iterations: 2 (840.0ms)

Iter	Nodes	Cost
0	217	2550
1	670	2395
2	3296	2109
done	5002	2109

prune642.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 47.0b

regimes287.0ms

Accuracy

60% (3.4b remaining)

Error of 52.3b against oracle of 48.8b and baseline of 57.4b

bsearch471.0ms

Steps

Iters	Range		Point
7	6.364187882694207e+150	2.636961861884747e+152	8.492055076595492e+150
7	-8.642262295924078e+80	-3.976749929960267e+79	-2.3529465240552972e+80

simplify16.0ms

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	50	128
1	77	88
done	77	88

end0.0ms

sample14.6s

Algorithm

intervals

Results

4.7s	2607×	body	2560	valid
4.1s	1865×	body	10240	exit
3.3s	3394×	body	1280	valid
1.1s	1081×	body	640	valid
790.0ms	9866×	pre	80	true
132.0ms	375×	body	320	valid
79.0ms	430×	body	80	valid
26.0ms	114×	body	160	valid