Details

sample248.0ms

Algorithm

intervals

Results

106.0ms	105×	body	2560	valid
58.0ms	65×	body	10240	exit
49.0ms	97×	body	1280	valid
9.0ms	30×	body	640	valid
6.0ms	321×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	10×	body	80	valid
0.0ms	3×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	239	24
4	653	24
5	2845	24
done	5001	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* b eps)) 1.0)
3.2b	(- (exp (* a eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

28.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series166.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
37.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify415.0ms

Counts

88 → 88

Iterations

Useful iterations: done (413.0ms)

Iter	Nodes	Cost
0	143	1364
1	345	1326
2	1271	1200
done	5002	1194

prune297.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 52.9b

localize26.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* (+ a b) eps)) 1.0)
5.0b	(* (* 1/6 (pow a 3)) eps)
7.8b	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))
14.3b	(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`*-un-lft-identity` `prod-exp`
9×	`associate-l`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `associate-r`
4×	`unpow-prod-down` `cbrt-unprod` `unswap-sqr`
2×	`pow-to-exp` `flip3-+` `associate-r/` `pow-exp` `-commutative` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `pow-prod-down` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (* 1/6 (pow a 3)) eps)
9.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))
39.0ms	(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (exp (* (+ a b) eps)) 1.0)
26.0ms	(* (* 1/6 (pow a 3)) eps)
61.0ms	(+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2)))
120.0ms	(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))

simplify942.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (366.0ms)

Iter	Nodes	Cost
0	151	1527
1	425	1424
2	1851	1265
done	5000	1265

prune393.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 52.8b

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* (+ a b) eps)) 1.0)
5.1b	(* (pow a 3) eps)
6.7b	(* eps (+ (* 1/2 (pow a 2)) (* 1/6 (* (pow a 3) eps))))
7.8b	(+ (* 1/2 (pow a 2)) (* 1/6 (* (pow a 3) eps)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`associate-l`
12×	`*-un-lft-identity`
11×	`add-exp-log`
10×	`add-cube-cbrt`
8×	`add-cbrt-cube` `add-log-exp`
6×	`pow1` `associate-r`
5×	`unswap-sqr`
4×	`unpow-prod-down` `cube-prod` `prod-exp`
2×	`flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 78

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 3) eps)
14.0ms	(* eps (+ (* 1/2 (pow a 2)) (* 1/6 (* (pow a 3) eps))))
4.0ms	(+ (* 1/2 (pow a 2)) (* 1/6 (* (pow a 3) eps)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (exp (* (+ a b) eps)) 1.0)
23.0ms	(* (pow a 3) eps)
123.0ms	(* eps (+ (* 1/2 (pow a 2)) (* 1/6 (* (pow a 3) eps))))
61.0ms	(+ (* 1/2 (pow a 2)) (* 1/6 (* (pow a 3) eps)))

simplify586.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (167.0ms)

Iter	Nodes	Cost
0	140	1278
1	373	1215
2	1300	1067
done	5000	1067

prune430.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 51.8b

localize30.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* (+ a b) eps)) 1.0)
6.5b	(* (* a a) eps)
6.7b	(* eps (+ (* 1/2 (pow a 2)) (* 1/6 (* a (* (* a a) eps)))))
7.8b	(+ (* 1/2 (pow a 2)) (* 1/6 (* a (* (* a a) eps))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (* a a) eps)
11.0ms	(* eps (+ (* 1/2 (pow a 2)) (* 1/6 (* a (* (* a a) eps)))))
4.0ms	(+ (* 1/2 (pow a 2)) (* 1/6 (* a (* (* a a) eps))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (* a a) eps)
124.0ms	(* eps (+ (* 1/2 (pow a 2)) (* 1/6 (* a (* (* a a) eps)))))
62.0ms	(+ (* 1/2 (pow a 2)) (* 1/6 (* a (* (* a a) eps))))

simplify648.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	131	1278
1	367	1138
2	1410	980
done	5000	980

prune376.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 51.8b

regimes124.0ms

Accuracy

59.8% (3.2b remaining)

Error of 53.1b against oracle of 49.9b and baseline of 57.9b

bsearch239.0ms

Steps

Iters	Range		Point
7	6.51529002498803e+73	8.5918266891709e+75	2.1920721130336317e+74
5	-6.59442686138714e+73	-2.3967451601057813e+73	-2.559152727206283e+73

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	140
1	78	140
done	78	140

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2610×	body	2560	valid
1.7s	1977×	body	10240	exit
1.7s	3486×	body	1280	valid
290.0ms	1067×	body	640	valid
173.0ms	9978×	pre	80	true
54.0ms	306×	body	320	valid
21.0ms	414×	body	80	valid
14.0ms	118×	body	160	valid