Details

sample134.0ms

Algorithm

intervals

Results

87.0ms	177×	body	1280	valid
11.0ms	261×	body	80	valid
11.0ms	41×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.8s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

10.0ms	(- (exp x) 2.0)
80.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(- (exp x) 2.0)
66.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify667.0ms

Counts

41 → 41

Iterations

Useful iterations: done (664.0ms)

Iter	Nodes	Cost
0	93	511
1	215	465
2	832	445
done	5001	433

prune163.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-exp-log`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 64

Calls

3 calls:

30.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
20.0ms	(* 1/360 (pow x 6))
25.0ms	(* 1/12 (pow x 4))

series206.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
78.0ms	(* 1/360 (pow x 6))
48.0ms	(* 1/12 (pow x 4))

simplify839.0ms

Counts

73 → 73

Iterations

Useful iterations: done (836.0ms)

Iter	Nodes	Cost
0	120	818
1	296	739
2	1143	695
done	5000	692

prune260.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
29.3b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.3b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `sqrt-prod` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
4×	`sqrt-div` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

12.0ms	(* 1/12 (pow x 4))
12.0ms	(* 1/12 (pow x 4))
45.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
45.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 1/12 (pow x 4))
70.0ms	(* 1/12 (pow x 4))
185.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
146.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify834.0ms

Counts

94 → 94

Iterations

Useful iterations: done (826.0ms)

Iter	Nodes	Cost
0	112	1420
1	270	1228
2	1046	1184
done	5001	1178

prune422.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 1/12 (pow x 4)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
1.7b	(log (exp (* 1/12 (pow x 4))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

9.0ms	(exp (* 1/12 (pow x 4)))
25.0ms	(* 1/360 (pow x 6))
21.0ms	(* 1/12 (pow x 4))
4.0ms	(log (exp (* 1/12 (pow x 4))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (* 1/12 (pow x 4)))
67.0ms	(* 1/360 (pow x 6))
48.0ms	(* 1/12 (pow x 4))
63.0ms	(log (exp (* 1/12 (pow x 4))))

simplify3.4s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	119	696
1	246	600
2	715	567
3	3826	552
done	5002	552

prune311.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.5b 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	15	33
1	19	33
done	19	33

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.4s	5601×	body	1280	valid
1.0s	8147×	body	80	valid
466.0ms	1244×	body	640	valid
109.0ms	660×	body	320	valid
76.0ms	327×	body	160	valid