Details

sample115.0ms

Algorithm

intervals

Results

79.0ms	186×	body	1280	valid
10.0ms	285×	body	80	valid
8.0ms	40×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify194.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	49	8
5	54	8
6	63	8
7	80	8
8	95	8
9	103	8
10	111	8
done	111	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

27.0ms	(- (exp x) 2.0)
90.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series85.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- (exp x) 2.0)
69.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify2.4s

Counts

71 → 71

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	124	914
1	274	729
2	709	628
3	3051	557
done	5000	554

prune197.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
12.0ms	(* 1/12 (pow x 4))

series254.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
148.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
45.0ms	(* 1/12 (pow x 4))

simplify1.4s

Counts

56 → 56

Iterations

Useful iterations: 3 (357.0ms)

Iter	Nodes	Cost
0	80	619
1	146	581
2	344	529
3	1278	526
done	5000	526

prune241.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (+ x x)) (* 2.0 2.0))
0.0b	(/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0))
0.0b	(+ (exp x) 2.0)
3.4b	(+ (/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))

rewrite780.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
40×	`times-frac`
38×	`add-sqr-sqrt`
29×	`fma-def`
28×	`add-cube-cbrt`
20×	`difference-of-squares`
13×	`distribute-lft-out`
12×	`exp-sum`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `flip3-+` `fma-neg` `prod-diff` `associate-/r*` `associate-/r/` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `flip3--` `div-sub` `frac-add` `sum-log` `flip--` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `exp-neg` `associate-+l-` `sub-neg` `frac-2neg` `exp-diff` `diff-log` `div-exp` `clear-num`

Counts

4 → 132

Calls

4 calls:

73.0ms	(- (exp (+ x x)) (* 2.0 2.0))
225.0ms	(/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0))
9.0ms	(+ (exp x) 2.0)
467.0ms	(+ (/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (exp (+ x x)) (* 2.0 2.0))
50.0ms	(/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0))
15.0ms	(+ (exp x) 2.0)
154.0ms	(+ (/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))

simplify2.2s

Counts

144 → 144

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	193	1988
1	472	1896
2	1522	1737
done	5000	1390

prune666.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt (exp (+ x x))) 2.0)
1.0b	(/ (- (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0)))
1.0b	(/ (+ (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0)))
57.1b	(fma (/ (+ (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0))) (/ (- (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0))) (exp (- x)))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
86×	`sqrt-prod`
77×	`times-frac`
61×	`add-cube-cbrt`
27×	`difference-of-squares`
21×	`prod-diff` `distribute-lft-out`
14×	`associate-/r*`
13×	`exp-sum`
11×	`associate-/l*`
9×	`distribute-lft-out--`
8×	`add-exp-log` `add-cbrt-cube`
7×	`fma-neg`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `associate-/l/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 195

Calls

4 calls:

100.0ms	(- (sqrt (exp (+ x x))) 2.0)
221.0ms	(/ (- (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0)))
200.0ms	(/ (+ (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0)))
1.0ms	(fma (/ (+ (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0))) (/ (- (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0))) (exp (- x)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (sqrt (exp (+ x x))) 2.0)
161.0ms	(/ (- (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0)))
121.0ms	(/ (+ (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0)))
288.0ms	(fma (/ (+ (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0))) (/ (- (sqrt (exp (+ x x))) 2.0) (sqrt (+ (exp x) 2.0))) (exp (- x)))

simplify1.3s

Counts

207 → 207

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	307	4741
1	679	4282
2	1641	3425
done	5000	3388

prune870.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
done	11	13

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.9s	5670×	body	1280	valid
477.0ms	8287×	body	80	valid
353.0ms	1222×	body	640	valid
150.0ms	630×	body	320	valid
33.0ms	305×	body	160	valid