Details

sample131.0ms

Algorithm

intervals

Results

84.0ms	173×	body	1280	valid
14.0ms	238×	body	80	valid
12.0ms	44×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify11.3s

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.6b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

21.0ms	(- (exp x) 2.0)
89.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series123.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(- (exp x) 2.0)
107.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.2s

Counts: 41 → 41

prune156.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

53.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
12.0ms	(* 1/360 (pow x 6))
12.0ms	(* 1/12 (pow x 4))

series467.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
226.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
97.0ms	(* 1/360 (pow x 6))
42.0ms	(* 1/12 (pow x 4))

simplify722.0ms

Counts: 87 → 87

prune353.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x)))) (- (- (exp x) 2.0) (exp (- x))))
0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
0.1b	(* (exp (- x)) (exp (- x)))
3.6b	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

148×	`frac-sub`
144×	`frac-times`
121×	`exp-neg`
119×	`flip3--` `flip--`
104×	`neg-sub0` `exp-diff`
95×	`*-un-lft-identity`
76×	`exp-prod`
74×	`associate-/l/`
72×	`associate-r/` `associate-l/`
64×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
24×	`distribute-rgt-neg-in` `times-frac`
21×	`distribute-lft-out--`
20×	`distribute-lft-neg-in`
18×	`pow1`
17×	`un-div-inv` `difference-of-squares`
16×	`pow-prod-down`
14×	`pow-sqr` `pow-prod-up`
10×	`swap-sqr` `add-cbrt-cube`
8×	`add-exp-log` `neg-mul-1` `associate-r` `associate-l`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `associate-/l*`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 333

Calls

4 calls:

262.0ms	(/ (- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x)))) (- (- (exp x) 2.0) (exp (- x))))
79.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
69.0ms	(* (exp (- x)) (exp (- x)))
57.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x)))) (- (- (exp x) 2.0) (exp (- x))))
36.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
18.0ms	(* (exp (- x)) (exp (- x)))
137.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

simplify671.0ms

Counts: 345 → 345

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2)
0.0b	(pow (exp x) 2)
0.1b	(pow (exp x) 3)
3.1b	(- (* (* (- (pow (exp x) 3) (pow 2.0 3)) (- (exp x) 2.0)) (* (exp x) (exp x))) (* (+ (* (exp x) (exp x)) (+ (* 2.0 2.0) (* (exp x) 2.0))) (* 1 (exp 0))))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-*l/`
16×	`frac-sub`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
12×	`pow-pow`
9×	`unpow-prod-down` `pow-unpow` `exp-prod`
8×	`frac-times` `flip3-+` `flip-+`
7×	`pow1`
6×	`add-log-exp`
5×	`add-cbrt-cube`
4×	`add-exp-log` `associate-*r/`
3×	`pow-to-exp` `cube-prod` `pow-exp` `sqr-pow`
2×	`unpow2`
1×	`cube-mult` `sub-neg` `diff-log` `unpow3` `rem-cube-cbrt`

Counts

4 → 96

Calls

4 calls:

10.0ms	(pow (exp x) 2)
9.0ms	(pow (exp x) 2)
9.0ms	(pow (exp x) 3)
351.0ms	(- (* (* (- (pow (exp x) 3) (pow 2.0 3)) (- (exp x) 2.0)) (* (exp x) (exp x))) (* (+ (* (exp x) (exp x)) (+ (* 2.0 2.0) (* (exp x) 2.0))) (* 1 (exp 0))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (exp x) 2)
22.0ms	(pow (exp x) 2)
41.0ms	(pow (exp x) 3)
351.0ms	(- (* (* (- (pow (exp x) 3) (pow 2.0 3)) (- (exp x) 2.0)) (* (exp x) (exp x))) (* (+ (* (exp x) (exp x)) (+ (* 2.0 2.0) (* (exp x) 2.0))) (* 1 (exp 0))))

simplify561.0ms

Counts: 108 → 108

prune868.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

39.5% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.7b

bsearch87.0ms

Steps

Iters	Range		Point
8	0.00022617661863457038	0.061554017742428864	0.0307964164762587

simplify1.3s

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.7s	5637×	body	1280	valid
493.0ms	8070×	body	80	valid
344.0ms	1207×	body	640	valid
119.0ms	667×	body	320	valid
36.0ms	312×	body	160	valid