Details

sample468.0ms

Algorithm

intervals

Results

144.0ms	84×	body	2560	valid
132.0ms	60×	body	10240	exit
99.0ms	107×	body	1280	valid
41.0ms	34×	body	640	valid
10.0ms	316×	pre	80	true
6.0ms	12×	body	320	valid
2.0ms	19×	body	80	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4020
4	765
3	258
2	101
1	40
0	17

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.4b	(- (exp (* a eps)) 1.0)
2.6b	(- (exp (* b eps)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite131.0ms

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-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

68.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
28.0ms	(- (exp (* a eps)) 1.0)
19.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* b eps)) 1.0)
61.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.6s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2610
1	540
0	221

prune968.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.1b

localize72.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* (pow a 3) (pow eps 3)) 1/6 (fma eps a (* (* a a) (* 1/2 (* eps eps))))) (- (exp (* b eps)) 1.0)))
3.8b	(- (exp (* (+ a b) eps)) 1.0)
13.3b	(* (* a a) (* 1/2 (* eps eps)))
16.0b	(* (pow a 3) (pow eps 3))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
39×	`add-cbrt-cube`
28×	`prod-exp`
25×	`pow1`
20×	`cbrt-unprod`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`pow-prod-down` `unswap-sqr`
14×	`unpow-prod-down` `cube-prod`
13×	`associate-r` `associate-l`
10×	`sqr-pow`
9×	`prod-diff`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-/r/` `*-commutative` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

37.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* (pow a 3) (pow eps 3)) 1/6 (fma eps a (* (* a a) (* 1/2 (* eps eps))))) (- (exp (* b eps)) 1.0)))
12.0ms	(- (exp (* (+ a b) eps)) 1.0)
64.0ms	(* (* a a) (* 1/2 (* eps eps)))
26.0ms	(* (pow a 3) (pow eps 3))

series1.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* (pow a 3) (pow eps 3)) 1/6 (fma eps a (* (* a a) (* 1/2 (* eps eps))))) (- (exp (* b eps)) 1.0)))
58.0ms	(- (exp (* (+ a b) eps)) 1.0)
52.0ms	(* (* a a) (* 1/2 (* eps eps)))
92.0ms	(* (pow a 3) (pow eps 3))

simplify496.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
1	915
0	293

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

26.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify2.3s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
3	2236
2	439
1	110
0	42

prune179.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* eps a)) 1.0))
1.4b	(- (exp (* eps a)) 1.0)
2.6b	(- (exp (* eps b)) 1.0)
3.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`add-cube-cbrt`
27×	`prod-diff`
25×	`times-frac`
15×	`distribute-lft-out--` `difference-of-squares`
10×	`add-log-exp`
9×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 138

Calls

4 calls:

53.0ms	(/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* eps a)) 1.0))
22.0ms	(- (exp (* eps a)) 1.0)
21.0ms	(- (exp (* eps b)) 1.0)
24.0ms	(- (exp (* (+ a b) eps)) 1.0)

series286.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* eps a)) 1.0))
43.0ms	(- (exp (* eps a)) 1.0)
46.0ms	(- (exp (* eps b)) 1.0)
66.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.2s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	1847
1	549
0	223

prune980.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

0% (3.5b remaining)

Error of 3.6b against oracle of 0.1b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample15.8s

Algorithm

intervals

Results

5.0s	2563×	body	2560	valid
4.0s	2004×	body	10240	exit
4.0s	3403×	body	1280	valid
1.1s	1087×	body	640	valid
637.0ms	343×	body	320	valid
413.0ms	10007×	pre	80	true
51.0ms	482×	body	80	valid
29.0ms	125×	body	160	valid