Details

sample67.0ms

Algorithm

intervals

Results

26.0ms	67×	body	640	valid
17.0ms	62×	body	1280	valid
6.0ms	177×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	15×	body	160	valid

simplify30.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.8b	(- (exp x) 1.0)

rewrite52.0ms

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:

37.0ms	(/ (- (exp x) 1.0) x)
11.0ms	(- (exp x) 1.0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify1.0s

Counts: 58 → 58

prune186.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
17×	`times-frac`
15×	`*-un-lft-identity`
13×	`associate-l`
12×	`prod-exp` `unswap-sqr`
11×	`add-cube-cbrt`
8×	`associate-r`
7×	`add-cbrt-cube` `add-log-exp`
6×	`unpow-prod-down` `div-exp`
4×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`
3×	`rec-exp` `1-exp` `associate-*l/` `sum-log`
2×	`pow1` `flip3-+` `frac-add` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `*-commutative` `div-inv`

Counts

2 → 71

Calls

2 calls:

57.0ms	(+ (* (/ 1 6) (pow x 2)) (+ (* (/ 1 2) x) 1))
42.0ms	(* (/ 1 6) (pow x 2))

series68.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (* (/ 1 6) (pow x 2)) (+ (* (/ 1 2) x) 1))
45.0ms	(* (/ 1 6) (pow x 2))

simplify814.0ms

Counts: 77 → 77

prune183.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* E (exp (+ (/ (pow x 2) 6) (* (/ 1 2) x))))
0.1b	(/ (pow x 2) 6)
0.3b	(log (* E (exp (+ (/ (pow x 2) 6) (* (/ 1 2) x)))))

rewrite699.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`pow1` `associate-/l*`
7×	`add-cbrt-cube`
4×	`associate-r` `prod-exp` `unpow2` `sqr-pow`
3×	`div-exp` `rem-log-exp` `associate-l` `associate-/r*` `add-log-exp`
2×	`e-exp-1` `pow-prod-down` `log-pow`
1×	`cbrt-undiv` `pow-to-exp` `log-prod` `frac-2neg` `exp-sum` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 82

Calls

3 calls:

392.0ms	(* E (exp (+ (/ (pow x 2) 6) (* (/ 1 2) x))))
18.0ms	(/ (pow x 2) 6)
284.0ms	(log (* E (exp (+ (/ (pow x 2) 6) (* (/ 1 2) x)))))

series215.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* E (exp (+ (/ (pow x 2) 6) (* (/ 1 2) x))))
29.0ms	(/ (pow x 2) 6)
152.0ms	(log (* E (exp (+ (/ (pow x 2) 6) (* (/ 1 2) x)))))

simplify656.0ms

Counts: 91 → 91

prune253.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
4.5b	(- (/ (exp x) x) (/ 1.0 x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

15.0ms	(/ (exp x) x)
59.0ms	(- (/ (exp x) x) (/ 1.0 x))

series118.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (exp x) x)
71.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify945.0ms

Counts: 56 → 56

prune131.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes28.0ms

Accuracy

98.8% (0.2b remaining)

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

bsearch20.0ms

Steps

Iters	Range		Point
5	-0.00021785999598854965	-9.497075983896804e-05	-0.00020145497221238883

simplify461.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

846.0ms	2197×	body	1280	valid
313.0ms	1692×	body	640	valid
228.0ms	5367×	body	80	valid
105.0ms	852×	body	320	valid
32.0ms	417×	body	160	valid