Details

sample525.0ms

Algorithm

intervals

Results

166.0ms	86×	body	2560	valid
155.0ms	119×	body	1280	valid
126.0ms	73×	body	10240	exit
17.0ms	28×	body	640	valid
10.0ms	329×	pre	80	true
2.0ms	6×	body	320	valid
1.0ms	12×	body	80	valid
1.0ms	5×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	245	24
4	699	24
5	3583	24
done	5002	24

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.9b	(- (exp (* a eps)) 1.0)
3.5b	(- (exp (* b eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite702.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-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-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

158.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
25.0ms	(- (exp (* a eps)) 1.0)
486.0ms	(- (exp (* b eps)) 1.0)
29.0ms	(- (exp (* (+ a b) eps)) 1.0)

series325.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
66.0ms	(- (exp (* a eps)) 1.0)
61.0ms	(- (exp (* b eps)) 1.0)
100.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	143	1364
1	358	1326
2	1782	1198
done	5001	1196

prune796.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 46.9b

localize95.0ms

Local error

Found 4 expressions with local error:

2.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.5b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow eps 2) (pow b 2))
15.9b	(* (pow eps 3) (pow b 3))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

197.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
19.0ms	(- (exp (* (+ a b) eps)) 1.0)
29.0ms	(* (pow eps 2) (pow b 2))
47.0ms	(* (pow eps 3) (pow b 3))

series3.2s

Counts

4 → 12

Calls

4 calls:

2.9s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
99.0ms	(- (exp (* (+ a b) eps)) 1.0)
60.0ms	(* (pow eps 2) (pow b 2))
120.0ms	(* (pow eps 3) (pow b 3))

simplify739.0ms

Counts

167 → 167

Iterations

Useful iterations: done (723.0ms)

Iter	Nodes	Cost
0	290	3682
1	888	3474
done	5001	2858

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite45.0ms

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:

44.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify1.5s

Counts

22 → 22

Iterations

Useful iterations: 3 (368.0ms)

Iter	Nodes	Cost
0	40	229
1	102	216
2	360	196
3	1364	194
done	5001	194

prune124.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 1 expressions with local error:

12.2b

(/ (+ a b) (* a b))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

42.0ms

(/ (+ a b) (* a b))

series68.0ms

Counts

1 → 3

Calls

1 calls:

68.0ms

(/ (+ a b) (* a b))

simplify2.8s

Counts

28 → 28

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	55	288
1	145	283
2	514	241
3	2276	241
done	5000	241

prune119.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes240.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
done	9	7

end0.0ms

sample19.9s

Algorithm

intervals

Results

6.5s	2601×	body	2560	valid
5.3s	2051×	body	10240	exit
4.7s	3448×	body	1280	valid
1.3s	10052×	pre	80	true
850.0ms	1053×	body	640	valid
195.0ms	313×	body	320	valid
61.0ms	458×	body	80	valid
36.0ms	128×	body	160	valid