Details

sample230.0ms

Algorithm

intervals

Results

67.0ms	67×	body	2560	valid
65.0ms	73×	body	10240	exit
54.0ms	113×	body	1280	valid
12.0ms	44×	body	640	valid
10.0ms	329×	pre	80	true
2.0ms	13×	body	320	valid
1.0ms	18×	body	80	valid
0.0ms	1×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	239	24
4	653	24
5	2971	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.6b	(- (exp (* a eps)) 1.0)
3.9b	(- (exp (* b eps)) 1.0)
6.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

21.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series329.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
39.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(- (exp (* b eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify829.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (183.0ms)

Iter	Nodes	Cost
0	174	1783
1	487	1741
2	2075	1427
done	5000	1427

prune320.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

15.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify2.4s

Counts

22 → 22

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	40	229
1	102	216
2	222	210
3	498	194
4	951	194
5	2256	194
done	5000	194

prune44.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (exp (* a eps)) 1.0)
3.9b	(log (exp (- (exp (* b eps)) 1.0)))
3.9b	(- (exp (* b eps)) 1.0)
6.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`add-cube-cbrt` `log-pow`
5×	`pow1` `log-prod` `exp-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
2×	`exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 62

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(log (exp (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series150.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(log (exp (- (exp (* b eps)) 1.0)))
37.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: 3 (478.0ms)

Iter	Nodes	Cost
0	134	863
1	275	801
2	688	724
3	2167	716
done	5001	716

prune273.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* 2 (* b eps))) (* 1.0 1.0)))
3.6b	(- (exp (* a eps)) 1.0)
3.8b	(- (exp (* 2 (* b eps))) (* 1.0 1.0))
6.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-l` `difference-of-squares`
4×	`frac-times` `associate-r`
3×	`diff-log` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

27.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* 2 (* b eps))) (* 1.0 1.0)))
4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* 2 (* b eps))) (* 1.0 1.0))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series187.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* 2 (* b eps))) (* 1.0 1.0)))
36.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* 2 (* b eps))) (* 1.0 1.0))
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify587.0ms

Counts

86 → 86

Iterations

Useful iterations: done (585.0ms)

Iter	Nodes	Cost
0	150	1631
1	372	1579
2	1406	1381
done	5000	1375

prune336.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes98.0ms

Accuracy

93.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.3b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	92
1	39	86
done	39	86

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2578×	body	2560	valid
1.7s	3399×	body	1280	valid
1.7s	1910×	body	10240	exit
296.0ms	1092×	body	640	valid
169.0ms	9910×	pre	80	true
66.0ms	361×	body	320	valid
23.0ms	442×	body	80	valid
15.0ms	128×	body	160	valid