Details

sample76.0ms

Algorithm

intervals

Results

25.0ms	91×	body	10240	exit
20.0ms	73×	body	1280	valid
8.0ms	47×	body	640	valid
3.0ms	29×	body	320	valid
3.0ms	100×	body	80	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
2.1b	(- (exp x) 1.0)

rewrite31.0ms

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

series88.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (exp x) (- (exp x) 1.0))
23.0ms	(- (exp x) 1.0)

simplify2.6s

Counts

57 → 57

Iterations

Useful iterations: 4 (957.0ms)

Iter	Nodes	Cost
0	91	640
1	181	614
2	410	579
3	804	577
4	2199	576
done	5000	576

prune147.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

46.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x))
21.0ms	(+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x)
45.0ms	(* (pow x 2) (+ (* 1/6 x) 1/2))
7.0ms	(* 1/6 x)

series205.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x))
46.0ms	(+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x)
86.0ms	(* (pow x 2) (+ (* 1/6 x) 1/2))
19.0ms	(* 1/6 x)

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	172	1552
1	429	1457
2	1375	1340
done	5000	1334

prune307.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
2.1b	(- 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:

10.0ms	(/ 1.0 (exp x))
33.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
16.0ms	(- 1 (/ 1.0 (exp x)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1.0 (exp x))
57.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
53.0ms	(- 1 (/ 1.0 (exp x)))

simplify5.7s

Counts

106 → 106

Iterations

Useful iterations: 4 (3.8s)

Iter	Nodes	Cost
0	162	1303
1	310	1155
2	580	1099
3	1282	1094
4	4161	1092
done	5001	1092

prune277.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp x))
0.6b	(/ (- (exp x) 1.0) (sqrt (exp x)))
0.7b	(/ (sqrt (exp x)) (/ (- (exp x) 1.0) (sqrt (exp x))))
2.1b	(- (exp x) 1.0)

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

444×	`times-frac`
315×	`add-sqr-sqrt`
314×	`*-un-lft-identity`
231×	`sqrt-prod`
214×	`add-cube-cbrt`
50×	`distribute-lft-out--` `difference-of-squares`
40×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-pow1` `div-exp`
3×	`exp-prod`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `pow1/2` `diff-log` `div-sub` `associate-/r/`

Counts

4 → 345

Calls

4 calls:

6.0ms	(sqrt (exp x))
58.0ms	(/ (- (exp x) 1.0) (sqrt (exp x)))
61.0ms	(/ (sqrt (exp x)) (/ (- (exp x) 1.0) (sqrt (exp x))))
26.0ms	(- (exp x) 1.0)

series186.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (exp x))
93.0ms	(/ (- (exp x) 1.0) (sqrt (exp x)))
51.0ms	(/ (sqrt (exp x)) (/ (- (exp x) 1.0) (sqrt (exp x))))
27.0ms	(- (exp x) 1.0)

simplify3.4s

Counts

357 → 357

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	370	8086
1	796	7254
2	2588	6648
done	5000	6479

prune724.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	18	17
done	18	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	2556×	body	10240	exit
682.0ms	2248×	body	1280	valid
485.0ms	1632×	body	640	valid
106.0ms	2906×	body	80	valid
99.0ms	824×	body	320	valid
31.0ms	392×	body	160	valid