Details

sample145.0ms

Algorithm

intervals

Results

71.0ms	122×	body	1280	valid
25.0ms	69×	body	640	valid
16.0ms	284×	body	80	valid
8.0ms	37×	body	320	valid
3.0ms	19×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	7	262
1	14	262
2	24	193
3	30	193
4	33	193
5	35	193
6	36	193
done	36	193

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.3b

localize25.0ms

Local error

Found 1 expressions with local error:

4.1b	(- (exp x) (exp (- x)))

rewrite22.0ms

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:

21.0ms

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

series45.0ms

Counts

1 → 3

Calls

1 calls:

45.0ms

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

simplify3.1s

Counts

17 → 17

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	46	6147
1	109	5644
2	260	4729
3	736	4612
4	2049	4572
done	5000	4542

prune114.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l` `prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`*-commutative`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp`

Counts

4 → 79

Calls

4 calls:

25.0ms	(* x (+ 2 (* (* x x) 1/3)))
19.0ms	(+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5)))
10.0ms	(* 1/60 (pow x 5))
15.0ms	(* (* x x) 1/3)

series278.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* x (+ 2 (* (* x x) 1/3)))
68.0ms	(+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5)))
64.0ms	(* 1/60 (pow x 5))
49.0ms	(* (* x x) 1/3)

simplify1.8s

Counts

91 → 91

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	142	28256
1	421	24948
2	1363	24867
done	5001	24627

prune399.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(exp (* -3 x))
0.0b	(exp (* 3 x))
4.0b	(- (exp (* 3 x)) (exp (* -3 x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`exp-prod`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`add-log-exp`
6×	`add-cbrt-cube`
4×	`pow-prod-down` `add-exp-log` `pow-sqr` `pow-prod-up`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`exp-to-pow` `rem-exp-log`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

17.0ms	(* (exp x) (exp x))
3.0ms	(exp (* -3 x))
3.0ms	(exp (* 3 x))
11.0ms	(- (exp (* 3 x)) (exp (* -3 x)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (exp x) (exp x))
12.0ms	(exp (* -3 x))
12.0ms	(exp (* 3 x))
54.0ms	(- (exp (* 3 x)) (exp (* -3 x)))

simplify2.5s

Counts

80 → 80

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	105	16557
1	236	14247
2	566	14027
3	1650	13465
done	5003	13105

prune378.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp 3) x) (exp (* -3 x))) (+ (+ (* (exp x) (exp x)) 1) (exp (* x -2))))
0.0b	(* (exp x) (exp x))
0.0b	(exp (* -3 x))
4.0b	(- (pow (exp 3) x) (exp (* -3 x)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
28×	`times-frac`
27×	`add-cube-cbrt`
19×	`exp-prod`
18×	`difference-of-squares`
11×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out` `add-log-exp`
7×	`associate-/l*`
6×	`unpow-prod-down` `add-exp-log` `distribute-lft-out--` `sqr-pow`
4×	`associate-/r*` `pow-prod-down` `pow-sqr` `pow-prod-up`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `exp-to-pow` `diff-log` `div-sub` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `rem-exp-log`

Counts

4 → 116

Calls

4 calls:

148.0ms	(/ (- (pow (exp 3) x) (exp (* -3 x))) (+ (+ (* (exp x) (exp x)) 1) (exp (* x -2))))
14.0ms	(* (exp x) (exp x))
3.0ms	(exp (* -3 x))
28.0ms	(- (pow (exp 3) x) (exp (* -3 x)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (- (pow (exp 3) x) (exp (* -3 x))) (+ (+ (* (exp x) (exp x)) 1) (exp (* x -2))))
15.0ms	(* (exp x) (exp x))
7.0ms	(exp (* -3 x))
129.0ms	(- (pow (exp 3) x) (exp (* -3 x)))

simplify2.6s

Counts

128 → 128

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	199	85110
1	498	69335
2	1696	69035
done	5002	68992

prune761.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	496
1	19	496
done	19	496

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	3431×	body	1280	valid
1.3s	2443×	body	640	valid
403.0ms	8142×	body	80	valid
230.0ms	1211×	body	320	valid
67.0ms	624×	body	160	valid