Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	83×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	193×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3
done	5001	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.9b	(- (exp (* a x)) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

4.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series55.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
41.0ms	(- (exp (* a x)) 1.0)

simplify82.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164
done	5002	164

prune93.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* a x)))
0.0b	(exp (* a x))
0.0b	(exp (* a x))
3.9b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `exp-to-pow` `sqrt-pow1` `sqrt-prod`
2×	`rem-exp-log`
1×	`rem-sqrt-square` `pow1/2` `fma-udef`

Counts

4 → 51

Calls

4 calls:

4.0ms	(sqrt (exp (* a x)))
4.0ms	(exp (* a x))
4.0ms	(exp (* a x))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series136.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (exp (* a x)))
14.0ms	(exp (* a x))
14.0ms	(exp (* a x))
85.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify48.0ms

Counts

63 → 63

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	124	289
1	381	252
2	1421	251
3	5001	250
done	5001	250

prune159.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))
3.9b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
3.9b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
3.9b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))
1.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series402.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))
86.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
86.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))
88.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify60.0ms

Counts

55 → 55

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	132	566
1	440	389
2	1877	377
3	5002	352
done	5002	352

prune227.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (exp (* a x)))
0.2b	(cbrt (exp (* a x)))
0.2b	(cbrt (exp (* a x)))
3.9b	(fma (sqrt (exp (* a x))) (sqrt (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (- 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (exp (* a x)))
2.0ms	(cbrt (exp (* a x)))
2.0ms	(cbrt (exp (* a x)))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (- 1.0))

series230.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (exp (* a x)))
51.0ms	(cbrt (exp (* a x)))
46.0ms	(cbrt (exp (* a x)))
86.0ms	(fma (sqrt (exp (* a x))) (sqrt (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (- 1.0))

simplify43.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	109	499
1	315	443
2	1165	437
3	5001	417
done	5001	417

prune406.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

regimes284.0ms

Accuracy

94.4% (1.2b remaining)

Error of 9.8b against oracle of 8.6b and baseline of 29.8b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	56
1	50	56
done	50	56

end0.0ms

sample969.0ms

Algorithm

intervals

Results

424.0ms	2729×	body	1280	valid
122.0ms	1269×	body	640	valid
104.0ms	5473×	body	80	valid
51.0ms	792×	body	320	valid
17.0ms	398×	body	160	valid