Details

sample403.0ms

Algorithm

intervals

Results

161.0ms	86×	body	2560	valid
97.0ms	71×	body	10240	exit
93.0ms	114×	body	1280	valid
15.0ms	33×	body	640	valid
8.0ms	327×	pre	80	true
2.0ms	5×	body	320	valid
2.0ms	16×	body	80	valid
0.0ms	2×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3569
4	699
3	245
2	101
1	40
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b	(- (exp (* a eps)) 1.0)
3.6b	(- (exp (* b eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

56.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
10.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series191.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
38.0ms	(- (exp (* a eps)) 1.0)
38.0ms	(- (exp (* b eps)) 1.0)
55.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1781
1	359
0	143

prune563.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 49.3b

localize95.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (exp (* a eps)) 1.0)
4.6b	(* (* (* (* 1/6 (* eps eps)) eps) (* b b)) b)
5.9b	(- (exp (* (+ a b) eps)) 1.0)
12.9b	(* (* (* 1/6 (* eps eps)) eps) (* b b))

rewrite933.0ms

Algorithm

rewrite-expression-head

Rules

78×	`pow1` `add-cbrt-cube` `add-exp-log`
57×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`associate-r`
2×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

16.0ms	(- (exp (* a eps)) 1.0)
684.0ms	(* (* (* (* 1/6 (* eps eps)) eps) (* b b)) b)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
213.0ms	(* (* (* 1/6 (* eps eps)) eps) (* b b))

series313.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (exp (* a eps)) 1.0)
97.0ms	(* (* (* (* 1/6 (* eps eps)) eps) (* b b)) b)
72.0ms	(- (exp (* (+ a b) eps)) 1.0)
84.0ms	(* (* (* 1/6 (* eps eps)) eps) (* b b))

simplify3.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	4146
1	545
0	175

prune688.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 48.7b

localize182.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (* (* eps (* eps (* eps 1/6))) b) b)
5.2b	(* (* (* eps (* eps (* eps 1/6))) b) b)
5.9b	(- (exp (* (+ a b) eps)) 1.0)
11.4b	(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))

rewrite15.3s

Algorithm

rewrite-expression-head

Rules

44×	`pow1` `add-cbrt-cube` `add-exp-log`
30×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`associate-r` `add-cube-cbrt` `add-log-exp`
2×	`associate-l` `*-commutative`
1×	`cbrt-prod` `sub-neg` `flip3--` `pow1/3` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 78

Calls

4 calls:

514.0ms	(* (* (* eps (* eps (* eps 1/6))) b) b)
549.0ms	(* (* (* eps (* eps (* eps 1/6))) b) b)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
14.2s	(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (* (* eps (* eps (* eps 1/6))) b) b)
81.0ms	(* (* (* eps (* eps (* eps 1/6))) b) b)
65.0ms	(- (exp (* (+ a b) eps)) 1.0)
127.0ms	(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))

simplify1.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2346
1	376
0	137

prune967.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 48.7b

localize211.0ms

Local error

Found 4 expressions with local error:

5.9b	(- (exp (* (+ a b) eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)
5.9b	(- (exp (* (+ a b) eps)) 1.0)
11.4b	(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))

rewrite14.8s

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 52

Calls

4 calls:

19.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
14.8s	(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (exp (* (+ a b) eps)) 1.0)
71.0ms	(- (exp (* (+ a b) eps)) 1.0)
74.0ms	(- (exp (* (+ a b) eps)) 1.0)
124.0ms	(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))

simplify763.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	689
1	163
0	74

prune816.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 48.7b

regimes380.0ms

Accuracy

53.1% (3.6b remaining)

Error of 52.9b against oracle of 49.3b and baseline of 56.9b

bsearch810.0ms

Steps

Iters	Range		Point
10	62695409.15370526	1.8979320083769524e+21	1.820560929758688e+21
10	-1.6112818967877033e+45	-2.0346378402041832e+34	-1.3170485397208287e+36

simplify26.0ms

Iterations

Iter	Nodes
done	82
1	82
0	56

end0.0ms

sample14.9s

Algorithm

intervals

Results

4.7s	2530×	body	2560	valid
4.2s	2042×	body	10240	exit
3.6s	3494×	body	1280	valid
1.1s	1075×	body	640	valid
476.0ms	10044×	pre	80	true
173.0ms	365×	body	320	valid
95.0ms	423×	body	80	valid
26.0ms	115×	body	160	valid