Details

sample222.0ms

Algorithm

intervals

Results

71.0ms	77×	body	2560	valid
61.0ms	119×	body	1280	valid
54.0ms	68×	body	10240	exit
10.0ms	34×	body	640	valid
6.0ms	324×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	10×	body	80	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	252	24
4	711	24
5	3154	24
done	5001	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize16.0ms

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)

rewrite50.0ms

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:

26.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
9.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)

series168.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* a eps)) 1.0)
35.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify630.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (202.0ms)

Iter	Nodes	Cost
0	221	3064
1	478	2615
2	1764	2162
done	5000	2162

prune433.0ms

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))

rewrite35.0ms

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:

4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))
11.0ms	(* (pow eps 3) (pow b 3))

series185.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))
67.0ms	(* (pow eps 3) (pow b 3))

simplify1.0s

Counts

182 → 182

Iterations

Useful iterations: 2 (324.0ms)

Iter	Nodes	Cost
0	250	2347
1	548	1998
2	2343	1658
done	5000	1658

prune768.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 49.6b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
40×	`add-sqr-sqrt`
34×	`prod-exp`
21×	`-un-lft-identity` `associate-l*`
20×	`add-cbrt-cube` `unswap-sqr`
19×	`add-cube-cbrt`
18×	`unpow-prod-down`
12×	`associate-r` `sqr-pow`
10×	`pow-to-exp` `pow-exp` `cbrt-unprod` `unpow2`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`pow-prod-down`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

22.0ms	(* (* (pow eps 3) (* b b)) b)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* (pow eps 3) (* b b))
8.0ms	(* (pow eps 2) (pow b 2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (* (pow eps 3) (* b b)) b)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
44.0ms	(* (pow eps 3) (* b b))
32.0ms	(* (pow eps 2) (pow b 2))

simplify1.0s

Counts

153 → 153

Iterations

Useful iterations: 2 (334.0ms)

Iter	Nodes	Cost
0	214	1883
1	502	1576
2	2142	1273
done	5000	1273

prune621.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 49.6b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
40×	`add-sqr-sqrt`
34×	`prod-exp`
21×	`-un-lft-identity` `associate-l*`
20×	`add-cbrt-cube` `unswap-sqr`
19×	`add-cube-cbrt`
18×	`unpow-prod-down`
12×	`associate-r` `sqr-pow`
10×	`pow-to-exp` `pow-exp` `cbrt-unprod` `unpow2`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
2×	`pow-prod-down`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

22.0ms	(* (* (pow eps 3) (* b b)) b)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (pow eps 3) (* b b))
12.0ms	(* (pow eps 2) (pow b 2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* (pow eps 3) (* b b)) b)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
44.0ms	(* (pow eps 3) (* b b))
33.0ms	(* (pow eps 2) (pow b 2))

simplify1.0s

Counts

153 → 153

Iterations

Useful iterations: 2 (332.0ms)

Iter	Nodes	Cost
0	214	1883
1	502	1576
2	2142	1273
done	5000	1273

prune642.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 49.6b

regimes198.0ms

Accuracy

51.7% (4.1b remaining)

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

bsearch316.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	48	132
1	61	132
done	61	132

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.5s	2599×	body	2560	valid
1.8s	2102×	body	10240	exit
1.7s	3417×	body	1280	valid
296.0ms	1057×	body	640	valid
177.0ms	10105×	pre	80	true
65.0ms	360×	body	320	valid
26.0ms	439×	body	80	valid
18.0ms	131×	body	160	valid