Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	70×	body	1280	valid
6.0ms	54×	body	640	valid
5.0ms	202×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	11×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize5.0ms

Local error

Found 1 expressions with local error:

3.1b	(- (exp x) 1.0)

rewrite11.0ms

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:

11.0ms

(- (exp x) 1.0)

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(- (exp x) 1.0)

simplify49.0ms

Counts: 17 → 17

prune54.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x 1/6) 1/2)
0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
3.8b	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

9.0ms	(+ (* x 1/6) 1/2)
34.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
7.0ms	(* x 1/6)
46.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

series175.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x 1/6) 1/2)
73.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
15.0ms	(* x 1/6)
48.0ms	(/ (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x) x)

simplify60.0ms

Counts: 101 → 101

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (- (exp x) 1.0) 3)
0.0b	(cbrt (pow (- (exp x) 1.0) 3))
3.1b	(- (exp x) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt`
5×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`pow1` `add-exp-log` `cube-div` `add-cbrt-cube`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 70

Calls

3 calls:

15.0ms	(pow (- (exp x) 1.0) 3)
15.0ms	(cbrt (pow (- (exp x) 1.0) 3))
10.0ms	(- (exp x) 1.0)

series74.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(pow (- (exp x) 1.0) 3)
20.0ms	(cbrt (pow (- (exp x) 1.0) 3))
15.0ms	(- (exp x) 1.0)

simplify29.0ms

Counts: 79 → 79

prune121.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow (- (exp x) 1.0) (sqrt 3)) (sqrt 3)))
0.1b	(pow (- (exp x) 1.0) (sqrt 3))
0.2b	(pow (pow (- (exp x) 1.0) (sqrt 3)) (sqrt 3))
3.1b	(- (exp x) 1.0)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

33×	`unpow-prod-down`
22×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`cbrt-prod`
12×	`pow-unpow`
7×	`add-exp-log`
6×	`sqrt-prod` `add-log-exp`
5×	`pow1` `pow-exp` `sqr-pow`
4×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`pow-to-exp`
2×	`pow-pow`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--`

Counts

4 → 85

Calls

4 calls:

26.0ms	(cbrt (pow (pow (- (exp x) 1.0) (sqrt 3)) (sqrt 3)))
16.0ms	(pow (- (exp x) 1.0) (sqrt 3))
33.0ms	(pow (pow (- (exp x) 1.0) (sqrt 3)) (sqrt 3))
11.0ms	(- (exp x) 1.0)

series892.0ms

Counts

4 → 12

Calls

4 calls:

454.0ms	(cbrt (pow (pow (- (exp x) 1.0) (sqrt 3)) (sqrt 3)))
132.0ms	(pow (- (exp x) 1.0) (sqrt 3))
287.0ms	(pow (pow (- (exp x) 1.0) (sqrt 3)) (sqrt 3))
19.0ms	(- (exp x) 1.0)

simplify42.0ms

Counts: 97 → 97

prune518.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch34.0ms

Steps

Iters	Range		Point
9	-108.06719872485291	-1.20447477858732e-06	-0.00011252250895241063

simplify1.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

498.0ms	2262×	body	1280	valid
280.0ms	1670×	body	640	valid
218.0ms	5539×	body	80	valid
68.0ms	781×	body	320	valid
24.0ms	447×	body	160	valid