Details

sample240.0ms

Algorithm

intervals

Results

108.0ms	105×	body	2560	valid
53.0ms	65×	body	10240	exit
44.0ms	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	253	24
4	722	24
5	3337	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize20.0ms

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)

rewrite45.0ms

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

series160.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
30.0ms	(- (exp (* b eps)) 1.0)
32.0ms	(- (exp (* a eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify771.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	221	3064
1	503	2615
2	2013	2158
done	5000	2158

prune414.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 52.9b

localize29.0ms

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))

rewrite46.0ms

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:

15.0ms	(* (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))

series258.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (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))
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
30.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify1.8s

Counts

200 → 200

Iterations

Useful iterations: 2 (259.0ms)

Iter	Nodes	Cost
0	305	4341
1	673	3908
2	3259	3408
done	5001	3408

prune774.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 51.7b

localize33.0ms

Local error

Found 4 expressions with local error:

3.9b	(* a (pow eps 3))
4.4b	(- (exp (* (+ a b) eps)) 1.0)
11.3b	(* (pow (* (cbrt a) (cbrt a)) 3) (* a (pow eps 3)))
15.4b	(* (pow a 2) (pow eps 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
45×	`add-sqr-sqrt`
44×	`prod-exp`
22×	`*-un-lft-identity`
21×	`associate-r`
20×	`add-cube-cbrt` `unswap-sqr`
19×	`unpow-prod-down` `associate-l` `pow-exp`
15×	`pow-to-exp`
13×	`add-cbrt-cube` `sqr-pow`
10×	`unpow2`
9×	`prod-diff`
6×	`add-log-exp`
5×	`cube-prod` `cbrt-unprod`
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 → 151

Calls

4 calls:

7.0ms	(* a (pow eps 3))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* (pow (* (cbrt a) (cbrt a)) 3) (* a (pow eps 3)))
9.0ms	(* (pow a 2) (pow eps 2))

series224.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* a (pow eps 3))
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
91.0ms	(* (pow (* (cbrt a) (cbrt a)) 3) (* a (pow eps 3)))
31.0ms	(* (pow a 2) (pow eps 2))

simplify1.8s

Counts

163 → 163

Iterations

Useful iterations: 2 (227.0ms)

Iter	Nodes	Cost
0	229	2073
1	556	1590
2	2781	1302
done	5000	1302

prune689.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 51.7b

localize31.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* 1 (* (- (pow (exp b) eps) 1.0) (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))))))
6.1b	(* (- (pow (exp b) eps) 1.0) (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))))
15.4b	(* (pow a 2) (pow eps 2))
16.1b	(* (pow a 3) (pow eps 3))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log` `add-sqr-sqrt`
36×	`prod-exp`
33×	`unswap-sqr`
31×	`add-cbrt-cube`
29×	`unpow-prod-down`
27×	`associate-l`
23×	`associate-r`
21×	`sqr-pow`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp` `cbrt-unprod`
10×	`div-exp` `unpow2`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `1-exp` `associate-r/` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `difference-of-squares`
2×	`cube-mult` `unpow3` `associate-/r/` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 177

Calls

4 calls:

43.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* 1 (* (- (pow (exp b) eps) 1.0) (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))))))
32.0ms	(* (- (pow (exp b) eps) 1.0) (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))))
9.0ms	(* (pow a 2) (pow eps 2))
11.0ms	(* (pow a 3) (pow eps 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

793.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* 1 (* (- (pow (exp b) eps) 1.0) (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))))))
241.0ms	(* (- (pow (exp b) eps) 1.0) (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))))
31.0ms	(* (pow a 2) (pow eps 2))
64.0ms	(* (pow a 3) (pow eps 3))

simplify391.0ms

Counts

189 → 189

Iterations

Useful iterations: done (385.0ms)

Iter	Nodes	Cost
0	333	4842
1	939	4514
done	5001	4466

prune903.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (2.7b remaining)

Error of 3.1b against oracle of 0.5b 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
1.8s	1977×	body	10240	exit
1.7s	3486×	body	1280	valid
291.0ms	1067×	body	640	valid
161.0ms	9978×	pre	80	true
54.0ms	306×	body	320	valid
22.0ms	414×	body	80	valid
14.0ms	118×	body	160	valid