Details

sample536.0ms

Algorithm

intervals

Results

212.0ms	86×	body	2560	valid
127.0ms	73×	body	10240	exit
119.0ms	119×	body	1280	valid
17.0ms	28×	body	640	valid
11.0ms	329×	pre	80	true
2.0ms	6×	body	320	valid
2.0ms	12×	body	80	valid
1.0ms	5×	body	160	valid

simplify3.4s

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	765	24
5	4008	24
done	5000	24

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.9b	(- (exp (* a eps)) 1.0)
3.5b	(- (exp (* b eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite242.0ms

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:

138.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* a eps)) 1.0)
29.0ms	(- (exp (* b eps)) 1.0)
31.0ms	(- (exp (* (+ a b) eps)) 1.0)

series286.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
55.0ms	(- (exp (* a eps)) 1.0)
60.0ms	(- (exp (* b eps)) 1.0)
80.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify2.3s

Counts

150 → 150

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	221	3064
1	539	2630
2	2596	2203
done	5000	2041

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 46.9b

localize98.0ms

Local error

Found 4 expressions with local error:

2.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))))
4.5b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow eps 2) (pow b 2))
15.9b	(* (pow eps 3) (pow b 3))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
23×	`*-un-lft-identity`
22×	`prod-exp`
21×	`add-cube-cbrt`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

87.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))))
40.0ms	(- (exp (* (+ a b) eps)) 1.0)
30.0ms	(* (pow eps 2) (pow b 2))
36.0ms	(* (pow eps 3) (pow b 3))

series2.8s

Counts

4 → 12

Calls

4 calls:

2.6s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))))
94.0ms	(- (exp (* (+ a b) eps)) 1.0)
70.0ms	(* (pow eps 2) (pow b 2))
106.0ms	(* (pow eps 3) (pow b 3))

simplify799.0ms

Counts

181 → 181

Iterations

Useful iterations: done (788.0ms)

Iter	Nodes	Cost
0	303	3696
1	837	3420
done	5000	2781

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

52.0ms

(+ (/ 1 b) (/ 1 a))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

(+ (/ 1 b) (/ 1 a))

simplify2.6s

Counts

37 → 37

Iterations

Useful iterations: 3 (640.0ms)

Iter	Nodes	Cost
0	42	245
1	110	231
2	460	211
3	2128	210
done	5001	210

prune268.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

12.2b

(/ (+ a b) (* b a))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

47.0ms

(/ (+ a b) (* b a))

series535.0ms

Counts

1 → 3

Calls

1 calls:

534.0ms

(/ (+ a b) (* b a))

simplify2.7s

Counts

30 → 30

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	58	304
1	148	298
2	513	256
3	2313	256
done	5000	256

prune147.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes343.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
done	9	7

end0.0ms

sample20.2s

Algorithm

intervals

Results

6.2s	3448×	body	1280	valid
6.1s	2601×	body	2560	valid
5.0s	2051×	body	10240	exit
893.0ms	1053×	body	640	valid
745.0ms	10052×	pre	80	true
143.0ms	313×	body	320	valid
90.0ms	128×	body	160	valid
67.0ms	458×	body	80	valid