Details

sample104.0ms

Algorithm

intervals

Results

51.0ms	100×	body	1280	valid
18.0ms	82×	body	640	valid
9.0ms	256×	body	80	valid
7.0ms	45×	body	320	valid
2.0ms	18×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	24	8
3	30	8
4	34	8
done	34	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.8b

localize19.0ms

Local error

Found 1 expressions with local error:

5.6b	(- (exp x) (exp (- x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 14

Calls

1 calls:

20.0ms

(- (exp x) (exp (- x)))

series88.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

(- (exp x) (exp (- x)))

simplify715.0ms

Counts

17 → 17

Iterations

Useful iterations: 3 (213.0ms)

Iter	Nodes	Cost
0	46	185
1	109	176
2	333	158
3	1367	157
done	5000	157

prune82.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
0.0b	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
0.1b	(* 1/60 (pow x 5))
0.1b	(* 1/3 (pow x 3))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `sum-log` `cube-prod` `sqr-pow`
2×	`pow-to-exp` `+-commutative` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

20.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
7.0ms	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
9.0ms	(* 1/60 (pow x 5))
14.0ms	(* 1/3 (pow x 3))

series518.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
263.0ms	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
91.0ms	(* 1/60 (pow x 5))
77.0ms	(* 1/3 (pow x 3))

simplify670.0ms

Counts

92 → 92

Iterations

Useful iterations: done (666.0ms)

Iter	Nodes	Cost
0	135	1095
1	381	953
2	1445	909
done	5000	908

prune417.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (- x)) (exp x))
0.0b	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp (- x)) (exp x)))
5.5b	(- (exp (+ x x)) (exp (* x -2)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
24×	`times-frac`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`distribute-lft-out`
7×	`add-log-exp`
6×	`exp-sum` `associate-/l*` `distribute-lft-out--`
5×	`add-cbrt-cube` `add-exp-log`
4×	`associate-/r*`
3×	`pow1`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 78

Calls

3 calls:

16.0ms	(+ (exp (- x)) (exp x))
171.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp (- x)) (exp x)))
81.0ms	(- (exp (+ x x)) (exp (* x -2)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (exp (- x)) (exp x))
118.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp (- x)) (exp x)))
57.0ms	(- (exp (+ x x)) (exp (* x -2)))

simplify980.0ms

Counts

87 → 87

Iterations

Useful iterations: done (976.0ms)

Iter	Nodes	Cost
0	150	1819
1	385	1764
2	1563	1615
done	5001	1582

prune395.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x)))
0.0b	(pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x))) 3)
0.1b	(cbrt (pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x))) 3))
5.5b	(- (exp (* 2 x)) (exp (* -2 x)))

rewrite613.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
101×	`add-sqr-sqrt`
100×	`times-frac`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`associate-/r*`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `cbrt-undiv` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `rem-cube-cbrt` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-div` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `rem-cbrt-cube`

Counts

4 → 200

Calls

4 calls:

90.0ms	(/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x)))
445.0ms	(pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x))) 3)
50.0ms	(cbrt (pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x))) 3))
11.0ms	(- (exp (* 2 x)) (exp (* -2 x)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x)))
184.0ms	(pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x))) 3)
140.0ms	(cbrt (pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp (- x)) (exp x))) 3))
44.0ms	(- (exp (* 2 x)) (exp (* -2 x)))

simplify2.1s

Counts

212 → 212

Iterations

Useful iterations: 2 (788.0ms)

Iter	Nodes	Cost
0	235	6460
1	826	5787
2	4527	5394
done	5000	5394

prune946.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	17
1	20	17
done	20	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	3453×	body	1280	valid
1.2s	2426×	body	640	valid
393.0ms	8001×	body	80	valid
294.0ms	1235×	body	320	valid
65.0ms	607×	body	160	valid