Details

sample123.0ms

Algorithm

intervals

Results

53.0ms	107×	body	1280	valid
24.0ms	79×	body	640	valid
14.0ms	282×	body	80	valid
7.0ms	36×	body	320	valid
2.0ms	19×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	18	8
2	26	8
3	34	8
4	36	8
done	36	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.1b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

15.0ms

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

series65.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

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

simplify5.7s

Counts

17 → 17

Iterations

Useful iterations: done (5.7s)

Iter	Nodes	Cost
0	46	185
1	231	174
done	5001	160

prune84.0ms

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))

rewrite85.0ms

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:

25.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
19.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
24.0ms	(* 1/60 (pow x 5))
14.0ms	(* 1/3 (pow x 3))

series418.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
178.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
74.0ms	(* 1/60 (pow x 5))
73.0ms	(* 1/3 (pow x 3))

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	137	1055
1	1042	929
done	5000	885

prune372.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize27.0ms

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))

rewrite42.0ms

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:

10.0ms	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
13.0ms	(* 1/60 (pow x 5))
17.0ms	(* 1/3 (pow x 3))

series353.0ms

Counts

3 → 9

Calls

3 calls:

216.0ms	(+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5)))
67.0ms	(* 1/60 (pow x 5))
70.0ms	(* 1/3 (pow x 3))

simplify2.7s

Counts

76 → 76

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	113	734
1	847	641
done	5001	605

prune287.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow (exp (- x)) 3)) (+ (+ (exp (+ x x)) (exp (- (+ x x)))) 1))
0.1b	(pow (exp x) 3)
0.1b	(pow (exp (- x)) 3)
6.0b	(- (pow (exp x) 3) (pow (exp (- x)) 3))

rewrite923.0ms

Algorithm

rewrite-expression-head

Rules

246×	`*-un-lft-identity`
214×	`add-sqr-sqrt`
125×	`times-frac`
112×	`difference-of-squares`
90×	`unpow-prod-down` `cube-prod`
78×	`distribute-lft-out`
58×	`sqr-pow`
46×	`add-cube-cbrt`
35×	`distribute-lft-out--`
25×	`associate-/l*`
15×	`pow-pow`
13×	`exp-prod`
8×	`add-cbrt-cube`
7×	`difference-cubes`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`associate-/r*`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`cube-div` `cube-mult` `pow-to-exp` `flip3--` `unpow3` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `neg-sub0` `exp-neg` `neg-mul-1` `sub-neg` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 267

Calls

4 calls:

808.0ms	(/ (- (pow (exp x) 3) (pow (exp (- x)) 3)) (+ (+ (exp (+ x x)) (exp (- (+ x x)))) 1))
10.0ms	(pow (exp x) 3)
18.0ms	(pow (exp (- x)) 3)
60.0ms	(- (pow (exp x) 3) (pow (exp (- x)) 3))

series502.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(/ (- (pow (exp x) 3) (pow (exp (- x)) 3)) (+ (+ (exp (+ x x)) (exp (- (+ x x)))) 1))
41.0ms	(pow (exp x) 3)
33.0ms	(pow (exp (- x)) 3)
185.0ms	(- (pow (exp x) 3) (pow (exp (- x)) 3))

simplify3.2s

Counts

279 → 279

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	285	8179
done	5000	7803

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes39.0ms

Accuracy

53.3% (0.2b remaining)

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

bsearch82.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.012882299779342181

simplify11.0ms

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	38	59
1	57	59
2	58	58
done	58	58

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.1s	3368×	body	1280	valid
1.1s	2481×	body	640	valid
519.0ms	8069×	body	80	valid
284.0ms	1250×	body	320	valid
73.0ms	636×	body	160	valid