Details

sample74.0ms

Algorithm

intervals

Results

51.0ms	179×	body	1280	valid
5.0ms	231×	body	80	valid
5.0ms	32×	body	640	valid
2.0ms	23×	body	320	valid
1.0ms	18×	body	160	valid

simplify28.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	52	8
5	69	8
6	97	8
7	160	8
8	329	8
9	1779	8
done	5000	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
6.5b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite36.0ms

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:

5.0ms	(- (exp x) 2.0)
29.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
55.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify3.4s

Counts

71 → 71

Iterations

Useful iterations: 3 (480.0ms)

Iter	Nodes	Cost
0	124	914
1	288	729
2	908	619
3	4859	557
done	5000	557

prune160.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

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 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
5.0ms	(* 1/12 (pow x 4))

series214.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
57.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
36.0ms	(* 1/12 (pow x 4))

simplify2.1s

Counts

56 → 56

Iterations

Useful iterations: 3 (286.0ms)

Iter	Nodes	Cost
0	80	619
1	148	581
2	498	529
3	2541	526
done	5000	526

prune141.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (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))))))
30.6b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

rewrite9.0ms

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 x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
5.0ms	(* 1/12 (pow x 4))
1.0ms	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
1.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
41.0ms	(* 1/12 (pow x 4))
59.0ms	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
99.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

simplify2.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (411.0ms)

Iter	Nodes	Cost
0	125	1186
1	240	1095
2	750	959
3	3438	956
done	5000	956

prune202.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b	(exp (* (cbrt (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))) (cbrt (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))))
30.6b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))
30.6b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))
30.6b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`rem-log-exp` `log-pow`
1×	`exp-prod` `exp-to-pow` `rem-exp-log`

Counts

4 → 54

Calls

4 calls:

1.0ms	(exp (* (cbrt (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))) (cbrt (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))))
1.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))
1.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))
1.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(exp (* (cbrt (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))) (cbrt (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))))
100.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))
96.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))
95.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

simplify662.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (198.0ms)

Iter	Nodes	Cost
0	232	2524
1	656	2375
2	2621	2118
done	5001	2118

prune308.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.6b 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

sample2.2s

Algorithm

intervals

Results

1.6s	5698×	body	1280	valid
184.0ms	1243×	body	640	valid
175.0ms	8117×	body	80	valid
53.0ms	588×	body	320	valid
19.0ms	314×	body	160	valid