Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	70×	body	1280	valid
11.0ms	59×	body	640	valid
6.0ms	161×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	16×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.9b	(- (exp x) 1.0)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

46.0ms	(/ (- (exp x) 1.0) x)
18.0ms	(- (exp x) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
22.0ms	(- (exp x) 1.0)

simplify78.0ms

Counts: 58 → 58

prune122.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

0.2b	(* 1/6 (pow x 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-l` `prod-exp` `add-cbrt-cube`
2×	`unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

12.0ms

(* 1/6 (pow x 2))

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(* 1/6 (pow x 2))

simplify95.0ms

Counts: 30 → 30

prune58.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
0.0b	(* (exp x) (exp x))
4.9b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
65.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
29.0ms	(* (exp x) (exp x))
24.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series140.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (exp x) 1.0)
85.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
14.0ms	(* (exp x) (exp x))
28.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify65.0ms

Counts: 99 → 99

prune311.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.1b	(- (pow (pow (exp (cbrt x)) (* 2 (cbrt x))) (cbrt x)) (* 1.0 1.0))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`cbrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
3×	`pow1/3`
2×	`sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
125.0ms	(- (pow (pow (exp (cbrt x)) (* 2 (cbrt x))) (cbrt x)) (* 1.0 1.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

273.0ms	(cbrt x)
282.0ms	(cbrt x)
264.0ms	(cbrt x)
1.3s	(- (pow (pow (exp (cbrt x)) (* 2 (cbrt x))) (cbrt x)) (* 1.0 1.0))

simplify37.0ms

Counts: 62 → 62

prune300.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch59.0ms

Steps

Iters	Range		Point
9	-0.002338049553438653	-8.574655782360099e-11	-0.0001245218611780339

simplify71.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

620.0ms	2297×	body	1280	valid
343.0ms	1617×	body	640	valid
210.0ms	5435×	body	80	valid
130.0ms	808×	body	320	valid
30.0ms	436×	body	160	valid