Details

sample243.0ms

Algorithm

intervals

Results

109.0ms	105×	body	2560	valid
54.0ms	65×	body	10240	exit
46.0ms	97×	body	1280	valid
8.0ms	30×	body	640	valid
5.0ms	321×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	10×	body	80	valid
0.0ms	3×	body	160	valid

simplify1.2s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* b eps)) 1.0)
3.2b	(- (exp (* a eps)) 1.0)
4.4b	(- (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:

29.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series161.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
36.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify612.0ms

Counts

150 → 150

Iterations

Useful iterations: done (607.0ms)

Iter	Nodes	Cost
0	221	3064
1	478	2615
2	1638	2243
done	5001	2198

prune426.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 52.9b

localize26.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
4.4b	(- (exp (* (+ a b) eps)) 1.0)
15.4b	(* (pow a 2) (pow eps 2))
16.1b	(* (pow a 3) (pow eps 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
27×	`prod-diff`
25×	`associate-r`
23×	`associate-l`
20×	`sqr-pow`
19×	`prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cbrt-cube` `unpow2`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `pow-prod-down` `*-commutative` `cbrt-unprod`
2×	`cube-mult` `flip3--` `unpow3` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 188

Calls

4 calls:

14.0ms	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow a 2) (pow eps 2))
11.0ms	(* (pow a 3) (pow eps 3))

series267.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify1.3s

Counts

200 → 200

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	305	4341
1	644	3908
2	2607	3435
done	5000	3408

prune734.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 51.9b

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
3.2b	(* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
4.4b	(- (exp (* (+ a b) eps)) 1.0)
15.4b	(* (pow a 2) (pow eps 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
27×	`prod-diff`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
14×	`unpow-prod-down` `prod-exp`
13×	`associate-r`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
10×	`unpow2` `sqr-pow`
6×	`pow1` `pow-to-exp` `associate-*r/` `pow-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
3×	`sub-neg` `fma-neg`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 154

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
15.0ms	(* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* (pow a 2) (pow eps 2))

series950.0ms

Counts

4 → 12

Calls

4 calls:

756.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
113.0ms	(* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow a 2) (pow eps 2))

simplify1.5s

Counts

166 → 166

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	314	5238
1	775	4865
2	3463	4044
done	5000	4017

prune623.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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:

19.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify1.9s

Counts

37 → 37

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	42	245
1	108	231
2	244	211
3	556	210
4	1237	210
5	3124	210
done	5000	210

prune72.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

0% (2.9b remaining)

Error of 3.1b against oracle of 0.2b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2610×	body	2560	valid
1.7s	1977×	body	10240	exit
1.7s	3486×	body	1280	valid
296.0ms	1067×	body	640	valid
171.0ms	9978×	pre	80	true
58.0ms	306×	body	320	valid
21.0ms	414×	body	80	valid
19.0ms	118×	body	160	valid