Details

sample345.0ms

Algorithm

intervals

Results

120.0ms	78×	body	2560	valid
70.0ms	103×	body	1280	valid
67.0ms	56×	body	10240	exit
16.0ms	39×	body	640	valid
7.0ms	312×	pre	80	true
3.0ms	12×	body	320	valid
2.0ms	20×	body	80	valid
1.0ms	4×	body	160	valid

simplify2.2s

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	699	24
5	3583	24
done	5002	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b	(- (exp (* a eps)) 1.0)
4.2b	(- (exp (* b eps)) 1.0)
6.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite192.0ms

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:

119.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
26.0ms	(- (exp (* a eps)) 1.0)
30.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series645.0ms

Counts

4 → 12

Calls

4 calls:

479.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
60.0ms	(- (exp (* a eps)) 1.0)
36.0ms	(- (exp (* b eps)) 1.0)
70.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify917.0ms

Counts

88 → 88

Iterations

Useful iterations: done (914.0ms)

Iter	Nodes	Cost
0	143	1364
1	358	1326
2	1782	1198
done	5001	1196

prune441.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.2b

localize53.0ms

Local error

Found 4 expressions with local error:

4.2b	(- (exp (* b eps)) 1.0)
6.4b	(- (exp (* (+ a b) eps)) 1.0)
11.2b	(* (pow a 2) (pow eps 2))
16.2b	(* (pow a 3) (pow eps 3))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`*-un-lft-identity` `prod-exp`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

28.0ms	(- (exp (* b eps)) 1.0)
24.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (pow a 2) (pow eps 2))
30.0ms	(* (pow a 3) (pow eps 3))

series295.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (exp (* b eps)) 1.0)
78.0ms	(- (exp (* (+ a b) eps)) 1.0)
50.0ms	(* (pow a 2) (pow eps 2))
107.0ms	(* (pow a 3) (pow eps 3))

simplify3.2s

Counts

150 → 150

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	211	1707
1	502	1532
2	3191	1330
done	5001	1323

prune974.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 47.3b

localize71.0ms

Local error

Found 4 expressions with local error:

3.5b	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
4.2b	(- (exp (* b eps)) 1.0)
6.4b	(- (exp (* (+ a b) eps)) 1.0)
11.2b	(* (pow a 2) (pow eps 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

64.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
25.0ms	(- (exp (* b eps)) 1.0)
28.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow a 2) (pow eps 2))

series319.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
50.0ms	(- (exp (* b eps)) 1.0)
68.0ms	(- (exp (* (+ a b) eps)) 1.0)
41.0ms	(* (pow a 2) (pow eps 2))

simplify2.8s

Counts

104 → 104

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	184	1503
1	464	1395
2	2837	1153
done	5001	1141

prune676.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 47.3b

localize57.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* a eps)) 1.0)
6.4b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))
15.9b	(* (pow eps 3) (pow b 3))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`*-un-lft-identity` `prod-exp`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

16.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
38.0ms	(* (pow eps 2) (pow b 2))
21.0ms	(* (pow eps 3) (pow b 3))

series312.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (exp (* a eps)) 1.0)
74.0ms	(- (exp (* (+ a b) eps)) 1.0)
59.0ms	(* (pow eps 2) (pow b 2))
125.0ms	(* (pow eps 3) (pow b 3))

simplify3.1s

Counts

150 → 150

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	207	1707
1	491	1532
2	3186	1328
done	5001	1323

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 46.5b

regimes244.0ms

Accuracy

36.8% (5.5b remaining)

Error of 54.6b against oracle of 49.1b and baseline of 57.8b

bsearch664.0ms

Steps

Iters	Range		Point
9	5.01402826469912e+113	1.9834641727302953e+120	1.0381429472904515e+117
7	-5.351987414543535e+167	-1.2795062131508902e+166	-1.2950505648577625e+166

simplify31.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	53	121
1	71	121
2	73	121
3	75	121
done	75	121

end0.0ms

sample15.3s

Algorithm

intervals

Results

5.4s	2632×	body	2560	valid
4.1s	3364×	body	1280	valid
3.6s	2022×	body	10240	exit
765.0ms	1091×	body	640	valid
656.0ms	10023×	pre	80	true
121.0ms	344×	body	320	valid
86.0ms	443×	body	80	valid
27.0ms	127×	body	160	valid