Details

sample223.0ms

Algorithm

intervals

Results

75.0ms	52×	body	10240	exit
46.0ms	327×	body	80	valid
36.0ms	43×	body	1280	valid
25.0ms	44×	body	640	valid
5.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	335	27
4	933	27
5	4084	27
done	5000	27

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (- 1.0 eps) x))
0.3b	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
0.3b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
1.5b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite433.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
46×	`times-frac`
24×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`distribute-lft-out--`
10×	`associate-/l*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r*` `distribute-lft-out`
4×	`pow1` `associate-/l/`
2×	`cbrt-undiv` `flip3--` `exp-to-pow` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `exp-prod` `flip3-+` `frac-sub` `flip-+` `rem-exp-log` `associate--r-`

Counts

4 → 109

Calls

4 calls:

9.0ms	(exp (* (- 1.0 eps) x))
65.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
84.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
270.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (* (- 1.0 eps) x))
74.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
80.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
308.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify2.9s

Counts

121 → 121

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	217	2790
1	517	2663
2	1271	2510
3	4228	2469
done	5000	2467

prune579.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

38.0ms

(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))

series116.0ms

Counts

1 → 3

Calls

1 calls:

116.0ms

(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))

simplify2.2s

Counts

36 → 36

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	69	467
1	161	440
2	544	385
3	2183	385
done	5000	385

prune111.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cbrt x) 2)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

7.0ms	(pow (cbrt x) 2)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

326.0ms	(pow (cbrt x) 2)
277.0ms	(cbrt x)
249.0ms	(cbrt x)
205.0ms	(cbrt x)

simplify1.4s

Counts

67 → 67

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	55	372
1	119	314
2	248	277
3	893	266
done	5001	263

prune277.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
1.6b	(log (exp (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`associate-l`
7×	`add-exp-log` `log-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`distribute-rgt-in` `sub-neg` `unpow-prod-down` `distribute-lft-in` `exp-sum` `add-cbrt-cube` `unswap-sqr`
3×	`pow1` `associate-r` `prod-exp` `log-pow` `add-log-exp`
2×	`associate-*r/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `pow-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 51

Calls

2 calls:

68.0ms	(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
12.0ms	(log (exp (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))))

series284.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
154.0ms	(log (exp (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))))

simplify2.4s

Counts

57 → 57

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	94	782
1	192	698
2	603	613
3	2347	613
done	5000	613

prune168.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes128.0ms

Accuracy

94.8% (0.8b remaining)

Error of 1.3b against oracle of 0.4b and baseline of 16.5b

bsearch181.0ms

Steps

Iters	Range		Point
6	1.0220978077804555e-07	1.0194597579740466e-06	9.944691288244345e-07

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	85
1	47	85
done	47	85

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.7s	9978×	body	80	valid
2.6s	1975×	body	10240	exit
1.8s	1747×	body	1280	valid
878.0ms	1239×	body	640	valid
258.0ms	647×	body	320	valid
82.0ms	316×	body	160	valid