Details

sample418.0ms

Algorithm

intervals

Results

173.0ms	85×	body	2560	valid
98.0ms	63×	body	10240	exit
84.0ms	97×	body	1280	valid
19.0ms	39×	body	640	valid
10.0ms	319×	pre	80	true
5.0ms	14×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	5×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	258	24
4	760	24
5	3738	24
done	5000	24

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b	(- (exp (* b eps)) 1.0)
5.0b	(- (exp (* a eps)) 1.0)
6.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

152.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
29.0ms	(- (exp (* b eps)) 1.0)
29.0ms	(- (exp (* a eps)) 1.0)
34.0ms	(- (exp (* (+ a b) eps)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
49.0ms	(- (exp (* b eps)) 1.0)
54.0ms	(- (exp (* a eps)) 1.0)
67.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.2s

Counts

150 → 150

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	221	3064
1	488	2615
2	1494	2203
done	5001	2038

prune670.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 47.3b

localize54.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (exp (* a eps)) 1.0)
5.1b	(* (* 1/6 (pow eps 3)) b)
6.6b	(- (exp (* (+ a b) eps)) 1.0)
12.9b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`associate-l`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `associate-r`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-exp` `-commutative` `flip--` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+`

Counts

4 → 110

Calls

4 calls:

17.0ms	(- (exp (* a eps)) 1.0)
48.0ms	(* (* 1/6 (pow eps 3)) b)
33.0ms	(- (exp (* (+ a b) eps)) 1.0)
67.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(* (* 1/6 (pow eps 3)) b)
97.0ms	(- (exp (* (+ a b) eps)) 1.0)
159.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify1.7s

Counts

122 → 122

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	216	2083
1	563	1788
2	1992	1537
done	5000	1463

prune972.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 46.7b

localize43.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (* 1/6 (pow eps 3)) b)
6.6b	(- (exp (* (+ a b) eps)) 1.0)
29.7b	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
29.7b	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt`
9×	`prod-diff` `add-cbrt-cube`
8×	`pow1`
7×	`prod-exp`
6×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-l` `pow-prod-down` `pow-exp` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 79

Calls

4 calls:

58.0ms	(* (* 1/6 (pow eps 3)) b)
31.0ms	(- (exp (* (+ a b) eps)) 1.0)
3.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
3.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 1/6 (pow eps 3)) b)
83.0ms	(- (exp (* (+ a b) eps)) 1.0)
187.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
199.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

simplify1.5s

Counts

91 → 91

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	154	1428
1	354	1237
2	1077	1105
done	5001	1052

prune872.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 46.7b

localize78.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (* 1/6 (pow eps 3)) b)
6.6b	(- (exp (* (+ a b) eps)) 1.0)
29.7b	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
29.7b	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt`
9×	`prod-diff` `add-cbrt-cube`
8×	`pow1`
7×	`prod-exp`
6×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-l` `pow-prod-down` `pow-exp` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 79

Calls

4 calls:

49.0ms	(* (* 1/6 (pow eps 3)) b)
30.0ms	(- (exp (* (+ a b) eps)) 1.0)
2.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
2.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* 1/6 (pow eps 3)) b)
88.0ms	(- (exp (* (+ a b) eps)) 1.0)
217.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
225.0ms	(sqrt (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

simplify1.6s

Counts

91 → 91

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	154	1428
1	354	1237
2	1077	1105
done	5001	1052

prune773.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 46.7b

regimes280.0ms

Accuracy

54.6% (3.9b remaining)

Error of 52.9b against oracle of 49.0b and baseline of 57.5b

bsearch685.0ms

Steps

Iters	Range		Point
9	2.0151688583404304e+101	2.940326713011017e+107	2.6102556639697233e+104
8	-5.625198100549435e+79	-4.694015096128857e+76	-1.3861963483449722e+79

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	51	156
1	67	156
done	67	156

end0.0ms

sample15.7s

Algorithm

intervals

Results

5.5s	2627×	body	2560	valid
4.2s	3480×	body	1280	valid
4.2s	1999×	body	10240	exit
598.0ms	1010×	body	640	valid
517.0ms	10001×	pre	80	true
164.0ms	334×	body	320	valid
45.0ms	434×	body	80	valid
26.0ms	117×	body	160	valid