Details

sample119.0ms

Algorithm

intervals

Results

68.0ms	176×	body	1280	valid
23.0ms	238×	body	80	valid
8.0ms	36×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.7s

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	56	8
5	62	8
6	71	8
7	88	8
8	248	8
9	788	8
10	3132	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
6.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite118.0ms

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:

25.0ms	(- (exp x) 2.0)
88.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp x) 2.0)
77.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify955.0ms

Counts

71 → 71

Iterations

Useful iterations: done (953.0ms)

Iter	Nodes	Cost
0	124	914
1	298	735
2	1173	637
done	5002	609

prune260.0ms

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))

rewrite31.0ms

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:

1.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
27.0ms	(* 1/12 (pow x 4))

series304.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
155.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
69.0ms	(* 1/12 (pow x 4))

simplify3.5s

Counts

56 → 56

Iterations

Useful iterations: 3 (819.0ms)

Iter	Nodes	Cost
0	80	619
1	155	581
2	507	529
3	3535	526
done	5001	526

prune262.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))
2.7b	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
30.5b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
17.0ms	(* 1/12 (pow x 4))
7.0ms	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
3.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
74.0ms	(* 1/12 (pow x 4))
86.0ms	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
133.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

simplify4.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	128	1140
1	254	1050
2	801	933
3	4970	930
done	5000	930

prune328.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (exp x) 2.0)
0.3b	(exp (log (+ (- (exp x) 2.0) (exp (- x)))))
6.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
18×	`prod-diff`
11×	`associate-+l+`
10×	`exp-diff` `add-log-exp`
8×	`frac-add`
6×	`log-div`
5×	`log-prod` `flip3--` `fma-def` `exp-sum` `flip--`
4×	`pow1` `neg-sub0` `exp-neg` `exp-prod` `distribute-lft-out` `distribute-lft-out--`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `log-pow` `rem-exp-log`

Counts

3 → 90

Calls

3 calls:

22.0ms	(- (exp x) 2.0)
50.0ms	(exp (log (+ (- (exp x) 2.0) (exp (- x)))))
89.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(- (exp x) 2.0)
75.0ms	(exp (log (+ (- (exp x) 2.0) (exp (- x)))))
70.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify916.0ms

Counts

99 → 99

Iterations

Useful iterations: done (910.0ms)

Iter	Nodes	Cost
0	168	1439
1	359	1154
2	1336	1015
done	5001	986

prune342.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.8s	5720×	body	1280	valid
385.0ms	1224×	body	640	valid
359.0ms	7931×	body	80	valid
81.0ms	599×	body	320	valid
27.0ms	309×	body	160	valid