Details

sample375.0ms

Algorithm

intervals

Results

121.0ms	107×	body	1280	valid
120.0ms	84×	body	2560	valid
79.0ms	60×	body	10240	exit
14.0ms	34×	body	640	valid
8.0ms	316×	pre	80	true
4.0ms	12×	body	320	valid
2.0ms	19×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.2b

localize30.0ms

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)

rewrite164.0ms

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:

108.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
19.0ms	(- (exp (* a eps)) 1.0)
24.0ms	(- (exp (* b eps)) 1.0)
10.0ms	(- (exp (* (+ a b) eps)) 1.0)

series219.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* a eps)) 1.0)
39.0ms	(- (exp (* b eps)) 1.0)
67.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify800.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1781
1	359
0	143

prune663.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
42×	`add-cbrt-cube`
40×	`prod-exp`
25×	`pow1`
22×	`cbrt-unprod`
15×	`pow-prod-down`
13×	`associate-r`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-/r/`
7×	`pow-to-exp` `pow-exp` `add-cube-cbrt`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/`
3×	`unpow-prod-down` `flip3-+` `cube-prod` `flip-+`
2×	`associate-l` `associate-l/` `-commutative` `associate-/l/`
1×	`cube-mult` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `unpow3` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

143.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* 1/6 (pow a 3)) (pow eps 3)) (* eps a)) (* (* a a) (* (* eps eps) 1/2))) (- (exp (* b eps)) 1.0)))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
91.0ms	(* (* a a) (* (* eps eps) 1/2))
37.0ms	(* (* 1/6 (pow a 3)) (pow eps 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* 1/6 (pow a 3)) (pow eps 3)) (* eps a)) (* (* a a) (* (* eps eps) 1/2))) (- (exp (* b eps)) 1.0)))
67.0ms	(- (exp (* (+ a b) eps)) 1.0)
60.0ms	(* (* a a) (* (* eps eps) 1/2))
113.0ms	(* (* 1/6 (pow a 3)) (pow eps 3))

simplify588.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
1	912
0	271

prune916.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

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` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+`

Counts

1 → 19

Calls

1 calls:

19.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify1.1s

Counts

22 → 22

Iterations

Iter	Nodes
done	5000
3	1500
2	381
1	102
0	40

prune87.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

78.0ms	(* (- (exp (* b eps)) 1.0) (- (exp (* a (+ eps eps))) (* 1.0 1.0)))
18.0ms	(- (exp (* a (+ eps eps))) (* 1.0 1.0))
18.0ms	(- (exp (* b eps)) 1.0)
19.0ms	(- (exp (* (+ a b) eps)) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (- (exp (* b eps)) 1.0) (- (exp (* a (+ eps eps))) (* 1.0 1.0)))
55.0ms	(- (exp (* a (+ eps eps))) (* 1.0 1.0))
45.0ms	(- (exp (* b eps)) 1.0)
64.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify904.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1883
1	421
0	163

prune883.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes197.0ms

Accuracy

0% (3.1b remaining)

Error of 3.6b against oracle of 0.5b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample15.4s

Algorithm

intervals

Results

5.4s	2563×	body	2560	valid
4.4s	3403×	body	1280	valid
3.4s	2004×	body	10240	exit
723.0ms	10007×	pre	80	true
649.0ms	1087×	body	640	valid
152.0ms	343×	body	320	valid
102.0ms	482×	body	80	valid
28.0ms	125×	body	160	valid