Details

sample442.0ms

Algorithm

intervals

Results

182.0ms	82×	body	2560	valid
109.0ms	113×	body	1280	valid
90.0ms	66×	body	10240	exit
16.0ms	29×	body	640	valid
9.0ms	322×	pre	80	true
5.0ms	13×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	3×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize40.0ms

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)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`add-cube-cbrt` `prod-diff`
10×	`add-log-exp`
9×	`fma-neg`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
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 → 107

Calls

4 calls:

28.0ms	(* (+ a b) eps)
30.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* a eps)) 1.0)
26.0ms	(- (exp (* (+ a b) eps)) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (+ a b) eps)
46.0ms	(- (exp (* b eps)) 1.0)
61.0ms	(- (exp (* a eps)) 1.0)
73.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify2.9s

Counts

119 → 119

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	193	1686
1	428	1415
2	1105	1167
3	3918	1035
done	5000	1034

prune569.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 47.2b

localize59.0ms

Local error

Found 4 expressions with local error:

4.3b	(- (exp (* (+ a b) eps)) 1.0)
5.0b	(fma eps (fma 1/2 (* eps (* a a)) a) (* 1/6 (* (pow a 3) (pow eps 3))))
7.3b	(* eps (* a a))
13.8b	(* (pow a 3) (pow eps 3))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
17×	`unswap-sqr`
15×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`associate-r`
12×	`prod-exp`
11×	`add-cbrt-cube`
10×	`sqr-pow`
9×	`pow1` `prod-diff`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`cube-mult` `unpow3` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

31.0ms	(- (exp (* (+ a b) eps)) 1.0)
0.0ms	(fma eps (fma 1/2 (* eps (* a a)) a) (* 1/6 (* (pow a 3) (pow eps 3))))
17.0ms	(* eps (* a a))
30.0ms	(* (pow a 3) (pow eps 3))

series370.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (exp (* (+ a b) eps)) 1.0)
158.0ms	(fma eps (fma 1/2 (* eps (* a a)) a) (* 1/6 (* (pow a 3) (pow eps 3))))
40.0ms	(* eps (* a a))
102.0ms	(* (pow a 3) (pow eps 3))

simplify1.6s

Counts

132 → 132

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	186	1752
1	405	1538
2	1294	1380
done	5000	1326

prune909.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 47.0b

localize48.0ms

Local error

Found 4 expressions with local error:

2.1b	(* eps (fma 1/2 (* eps (* a a)) a))
2.3b	(- (exp (* b eps)) 1.0)
4.3b	(- (exp (* (+ a b) eps)) 1.0)
7.3b	(* eps (* a a))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`fma-neg` `associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `*-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 99

Calls

4 calls:

12.0ms	(* eps (fma 1/2 (* eps (* a a)) a))
19.0ms	(- (exp (* b eps)) 1.0)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)
41.0ms	(* eps (* a a))

series236.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* eps (fma 1/2 (* eps (* a a)) a))
49.0ms	(- (exp (* b eps)) 1.0)
58.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* eps (* a a))

simplify2.8s

Counts

111 → 111

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	180	1528
1	391	1338
2	952	1113
3	3359	1020
done	5001	964

prune662.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 46.5b

localize38.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (* (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (fma 1/2 (* eps (* a a)) a))) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
4.3b	(- (exp (* (+ a b) eps)) 1.0)
7.3b	(* eps (* a a))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
27×	`pow1` `add-exp-log`
21×	`add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-log-exp`
6×	`fma-neg` `associate-r`
4×	`expm1-log1p-u` `sub-neg` `associate-l` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`diff-log` `associate-r/` `-commutative`
1×	`unswap-sqr`

Counts

4 → 132

Calls

4 calls:

248.0ms	(* (* (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (fma 1/2 (* eps (* a a)) a))) (- (exp (* b eps)) 1.0))
30.0ms	(- (exp (* b eps)) 1.0)
27.0ms	(- (exp (* (+ a b) eps)) 1.0)
28.0ms	(* eps (* a a))

series292.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (fma 1/2 (* eps (* a a)) a))) (- (exp (* b eps)) 1.0))
34.0ms	(- (exp (* b eps)) 1.0)
69.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* eps (* a a))

simplify1.9s

Counts

144 → 144

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	246	3706
1	619	3337
2	2275	2508
done	5000	2135

prune638.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 46.5b

regimes305.0ms

Accuracy

55.6% (3.3b remaining)

Error of 52.1b against oracle of 48.8b and baseline of 56.3b

bsearch521.0ms

Steps

Iters	Range		Point
5	1.7897742140858872e+53	5.1194650287633095e+53	1.8117384557919386e+53
8	-2.0477085041669336e+133	-5.2045971803048284e+128	-5.30817544204267e+128

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	43	106
1	60	77
done	60	77

end0.0ms

sample16.0s

Algorithm

intervals

Results

5.3s	2607×	body	2560	valid
4.7s	1865×	body	10240	exit
4.1s	3394×	body	1280	valid
720.0ms	1081×	body	640	valid
391.0ms	9866×	pre	80	true
140.0ms	375×	body	320	valid
47.0ms	430×	body	80	valid
28.0ms	114×	body	160	valid