Details

sample57.0ms

Algorithm

intervals

Results

18.0ms	103×	body	10240	exit
18.0ms	92×	body	1280	valid
5.0ms	45×	body	640	valid
2.0ms	87×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

18.0ms	(/ (exp x) (- (exp x) 1.0))
10.0ms	(- (exp x) 1.0)

series64.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (exp x) (- (exp x) 1.0))
32.0ms	(- (exp x) 1.0)

simplify64.0ms

Counts: 57 → 57

prune133.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
0.0b	(+ (* 1/12 x) (/ 1 x))
0.4b	(* 1/12 x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

31.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
12.0ms	(+ (* 1/12 x) (/ 1 x))
11.0ms	(* 1/12 x)

series78.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
46.0ms	(+ (* 1/12 x) (/ 1 x))
16.0ms	(* 1/12 x)

simplify100.0ms

Counts: 52 → 52

prune88.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
3.6b	(- 1 (/ 1.0 (exp x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`times-frac`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 97

Calls

3 calls:

36.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
7.0ms	(/ 1.0 (exp x))
16.0ms	(- 1 (/ 1.0 (exp x)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
15.0ms	(/ 1.0 (exp x))
38.0ms	(- 1 (/ 1.0 (exp x)))

simplify34.0ms

Counts: 106 → 106

prune157.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.4b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
0.5b	(/ (exp x) (/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))))
3.5b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

644×	`add-sqr-sqrt`
618×	`times-frac`
406×	`*-un-lft-identity`
272×	`difference-of-squares`
236×	`add-cube-cbrt`
207×	`unpow-prod-down` `cube-prod`
137×	`sqr-pow`
85×	`distribute-lft-out--`
84×	`associate-/r*`
28×	`associate-/l*`
17×	`difference-cubes`
12×	`add-cbrt-cube`
11×	`associate-/r/`
9×	`add-exp-log`
6×	`div-inv` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `pow-pow` `div-exp`
3×	`pow-unpow` `exp-prod`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `sub-neg` `diff-log` `unpow3` `div-sub` `pow-exp` `rem-cube-cbrt`

Counts

4 → 522

Calls

4 calls:

5.0ms	(pow (exp x) 3)
115.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
111.0ms	(/ (exp x) (/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))))
31.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series281.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (exp x) 3)
97.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
121.0ms	(/ (exp x) (/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))))
39.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify121.0ms

Counts: 534 → 534

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes51.0ms

Accuracy

97% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.1b

bsearch1.0ms

simplify1.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

950.0ms	2644×	body	10240	exit
478.0ms	2267×	body	1280	valid
213.0ms	1633×	body	640	valid
73.0ms	829×	body	320	valid
71.0ms	2848×	body	80	valid
24.0ms	426×	body	160	valid