Details

sample88.0ms

Algorithm

intervals

Results

46.0ms	107×	body	1280	valid
15.0ms	79×	body	640	valid
8.0ms	282×	body	80	valid
4.0ms	36×	body	320	valid
1.0ms	19×	body	160	valid

simplify17.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.1b

localize7.0ms

Local error

Found 1 expressions with local error:

6.3b	(- (exp x) (exp (- x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 14

Calls

1 calls:

18.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify1.7s

Counts

17 → 17

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	46	185
1	100	176
2	231	158
3	532	157
4	1593	157
done	5000	157

prune91.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
0.0b	(+ (* 1/60 (pow x 5)) (* 2 x))
0.1b	(* 1/60 (pow x 5))
0.2b	(* 1/3 (pow x 3))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

23.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
27.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
22.0ms	(* 1/60 (pow x 5))
24.0ms	(* 1/3 (pow x 3))

series305.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
143.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
49.0ms	(* 1/60 (pow x 5))
42.0ms	(* 1/3 (pow x 3))

simplify863.0ms

Counts

92 → 92

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	137	1055
1	359	917
2	1157	873
done	5001	872

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
0.1b	(* 1/60 (pow x 5))
0.2b	(* 1/3 (pow x 3))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

18.0ms	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
25.0ms	(* 1/60 (pow x 5))
14.0ms	(* 1/3 (pow x 3))

series321.0ms

Counts

3 → 9

Calls

3 calls:

207.0ms	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
60.0ms	(* 1/60 (pow x 5))
53.0ms	(* 1/3 (pow x 3))

simplify3.2s

Counts

76 → 76

Iterations

Useful iterations: 3 (884.0ms)

Iter	Nodes	Cost
0	113	734
1	273	633
2	771	597
3	3519	596
done	5001	596

prune259.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

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))))
6.5b	(- (exp (+ x x)) (exp (* x -2)))

rewrite300.0ms

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-exp-log` `add-cbrt-cube`
4×	`associate-/r*`
3×	`pow1`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 78

Calls

3 calls:

14.0ms	(+ (exp x) (exp (- x)))
219.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp x) (exp (- x))))
61.0ms	(- (exp (+ x x)) (exp (* x -2)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (exp x) (exp (- x)))
109.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp x) (exp (- x))))
75.0ms	(- (exp (+ x x)) (exp (* x -2)))

simplify2.2s

Counts

87 → 87

Iterations

Useful iterations: 3 (937.0ms)

Iter	Nodes	Cost
0	149	1819
1	359	1763
2	913	1613
3	2809	1576
done	5000	1576

prune331.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

53.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.6b

bsearch42.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.012882299779342181

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	47
1	37	47
done	37	47

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	3368×	body	1280	valid
875.0ms	8069×	body	80	valid
740.0ms	2481×	body	640	valid
279.0ms	1250×	body	320	valid
71.0ms	636×	body	160	valid