Details

sample229.0ms

Algorithm

intervals

Results

73.0ms	77×	body	2560	valid
60.0ms	68×	body	10240	exit
58.0ms	119×	body	1280	valid
10.0ms	34×	body	640	valid
6.0ms	324×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	10×	body	80	valid
1.0ms	5×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	252	24
4	711	24
5	3154	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
4.8b	(- (exp (* b eps)) 1.0)
6.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite48.0ms

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:

27.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
6.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series170.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
38.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify690.0ms

Counts

150 → 150

Iterations

Useful iterations: done (685.0ms)

Iter	Nodes	Cost
0	221	3064
1	478	2615
2	1639	2215
done	5000	2170

prune435.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 50.5b

localize28.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* a eps)) 1.0)
6.0b	(- (exp (* (+ a b) eps)) 1.0)
16.9b	(* (pow eps 2) (pow b 2))
18.6b	(* (pow eps 3) (pow b 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))
12.0ms	(* (pow eps 3) (pow b 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))
65.0ms	(* (pow eps 3) (pow b 3))

simplify1.1s

Counts

182 → 182

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	250	2347
1	548	1998
2	2054	1676
done	5001	1658

prune737.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 49.6b

localize36.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* (pow eps 3) (* b b)) (pow (cbrt b) 3))
6.0b	(- (exp (* (+ a b) eps)) 1.0)
13.2b	(* (pow eps 3) (* b b))
16.9b	(* (pow eps 2) (pow b 2))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-exp-log`
66×	`prod-exp`
44×	`add-sqr-sqrt`
27×	`associate-r`
25×	`*-un-lft-identity`
24×	`unpow-prod-down`
23×	`add-cube-cbrt`
21×	`pow-to-exp` `associate-l` `pow-exp`
20×	`add-cbrt-cube` `unswap-sqr`
13×	`sqr-pow`
10×	`cube-prod` `cbrt-unprod` `unpow2`
9×	`prod-diff`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`cube-mult` `unpow3`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

29.0ms	(* (* (pow eps 3) (* b b)) (pow (cbrt b) 3))
6.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (pow eps 3) (* b b))
9.0ms	(* (pow eps 2) (pow b 2))

series217.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (* (pow eps 3) (* b b)) (pow (cbrt b) 3))
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
39.0ms	(* (pow eps 3) (* b b))
36.0ms	(* (pow eps 2) (pow b 2))

simplify1.3s

Counts

181 → 181

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	251	2385
1	618	1850
2	2305	1529
done	5000	1520

prune902.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 49.6b

localize35.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* (pow eps 3) (* b b)) (pow (cbrt b) 3))
6.0b	(- (exp (* (+ a b) eps)) 1.0)
13.2b	(* (pow eps 3) (* b b))
16.9b	(* (pow eps 2) (pow b 2))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-exp-log`
66×	`prod-exp`
44×	`add-sqr-sqrt`
27×	`associate-r`
25×	`*-un-lft-identity`
24×	`unpow-prod-down`
23×	`add-cube-cbrt`
21×	`pow-to-exp` `associate-l` `pow-exp`
20×	`add-cbrt-cube` `unswap-sqr`
13×	`sqr-pow`
10×	`cube-prod` `cbrt-unprod` `unpow2`
9×	`prod-diff`
6×	`cbrt-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`cube-mult` `unpow3`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

28.0ms	(* (* (pow eps 3) (* b b)) (pow (cbrt b) 3))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
13.0ms	(* (pow eps 3) (* b b))
9.0ms	(* (pow eps 2) (pow b 2))

series212.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (* (pow eps 3) (* b b)) (pow (cbrt b) 3))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
41.0ms	(* (pow eps 3) (* b b))
32.0ms	(* (pow eps 2) (pow b 2))

simplify1.3s

Counts

181 → 181

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	251	2385
1	618	1850
2	2305	1529
done	5000	1520

prune729.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 49.6b

regimes202.0ms

Accuracy

51.8% (4.1b remaining)

Error of 53.4b against oracle of 49.3b and baseline of 57.9b

bsearch314.0ms

Steps

Iters	Range		Point
11	3.9777289923527025e+45	6.762908678833405e+72	6.566435701181497e+46
5	-2.350670412092924e+26	-9.509086209243448e+25	-2.3194785649155656e+26

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	46	135
1	61	92
done	61	92

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.6s	2599×	body	2560	valid
1.8s	2102×	body	10240	exit
1.7s	3417×	body	1280	valid
298.0ms	1057×	body	640	valid
175.0ms	10105×	pre	80	true
68.0ms	360×	body	320	valid
24.0ms	439×	body	80	valid
16.0ms	131×	body	160	valid