Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	63×	body	1280	valid
9.0ms	62×	body	640	valid
5.0ms	171×	body	80	valid
3.0ms	33×	body	320	valid
1.0ms	12×	body	160	valid

simplify16.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.6b	(- (exp x) 1.0)

rewrite77.0ms

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:

55.0ms	(/ (- (exp x) 1.0) x)
19.0ms	(- (exp x) 1.0)

series69.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- (exp x) 1.0) x)
20.0ms	(- (exp x) 1.0)

simplify772.0ms

Counts: 58 → 58

prune144.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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:

22.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
12.0ms	(* 1/6 (pow x 2))

series55.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
31.0ms	(* 1/6 (pow x 2))

simplify558.0ms

Counts: 46 → 46

prune96.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.1b	(* 1/6 (pow x 3))
2.4b	(/ (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)) x)
11.6b	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`associate-r`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`times-frac` `add-log-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sqr-pow`
3×	`associate-/r` `sum-log` `associate-/l`
2×	`pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unpow2`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `associate-+r+` `frac-2neg` `unpow3` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

13.0ms	(* 1/2 (pow x 2))
15.0ms	(* 1/6 (pow x 3))
82.0ms	(/ (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)) x)
27.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

series146.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/2 (pow x 2))
38.0ms	(* 1/6 (pow x 3))
49.0ms	(/ (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)) x)
29.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

simplify804.0ms

Counts: 112 → 112

prune314.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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))
2.7b	(/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)))
11.6b	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

rewrite194.0ms

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:

71.0ms	(/ 1 (/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))))
20.0ms	(* 1/6 (pow x 3))
60.0ms	(/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)))
32.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

series233.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1 (/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))))
52.0ms	(* 1/6 (pow x 3))
71.0ms	(/ x (+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x)))
49.0ms	(+ (* 1/2 (pow x 2)) (+ (* 1/6 (pow x 3)) x))

simplify1.3s

Counts: 169 → 169

prune542.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.0b

bsearch53.0ms

Steps

Iters	Range		Point
9	-31.62993370098301	-9.856482395706948e-05	-0.0012956373129975165

simplify749.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

664.0ms	1679×	body	640	valid
595.0ms	2250×	body	1280	valid
202.0ms	5486×	body	80	valid
84.0ms	796×	body	320	valid
31.0ms	469×	body	160	valid