Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	77×	body	1280	valid
5.0ms	37×	body	640	valid
5.0ms	196×	body	80	valid
2.0ms	29×	body	320	valid
1.0ms	14×	body	160	valid

simplify17.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.0b	(- (exp x) 1.0)

rewrite76.0ms

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:

61.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify917.0ms

Counts: 58 → 58

prune168.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

33.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
12.0ms	(* 1/6 (pow x 2))

series76.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
53.0ms	(* 1/6 (pow x 2))

simplify503.0ms

Counts: 46 → 46

prune102.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/6 (pow x 3)) x)
0.1b	(* 1/6 (pow x 3))
3.5b	(/ (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)) x)
13.6b	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`add-exp-log` `add-log-exp`
9×	`times-frac`
8×	`add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `cube-prod` `sum-log` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `associate-+r+` `frac-2neg` `unpow3` `div-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 84

Calls

4 calls:

19.0ms	(+ (* 1/6 (pow x 3)) x)
30.0ms	(* 1/6 (pow x 3))
106.0ms	(/ (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)) x)
47.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

series257.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (* 1/6 (pow x 3)) x)
47.0ms	(* 1/6 (pow x 3))
63.0ms	(/ (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)) x)
32.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

simplify855.0ms

Counts: 96 → 96

prune347.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))))
0.1b	(* 1/6 (pow x 3))
3.9b	(/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)))
13.6b	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
67×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`associate-r`
11×	`associate-/r/`
9×	`add-log-exp`
8×	`div-exp`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r+` `pow-flip` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 157

Calls

4 calls:

101.0ms	(/ 1 (/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))))
27.0ms	(* 1/6 (pow x 3))
59.0ms	(/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)))
42.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))))
53.0ms	(* 1/6 (pow x 3))
71.0ms	(/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)))
36.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

simplify1.3s

Counts: 169 → 169

prune670.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 19.9b

bsearch29.0ms

Steps

Iters	Range		Point
8	-0.06705623481545048	-1.7104155354788486e-05	-0.002149798604784803

simplify780.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

727.0ms	2289×	body	1280	valid
347.0ms	1647×	body	640	valid
247.0ms	5520×	body	80	valid
142.0ms	825×	body	320	valid
34.0ms	429×	body	160	valid