Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	83×	body	1280	valid
7.0ms	43×	body	640	valid
3.0ms	193×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify60.0ms

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)

rewrite19.0ms

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)

series52.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify81.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (77.0ms)

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

prune84.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize7.0ms

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))

rewrite15.0ms

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:

3.0ms	(sqrt (exp (* a x)))
4.0ms	(exp (* a x))
7.0ms	(exp (* a x))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series131.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* a x)))
13.0ms	(exp (* a x))
18.0ms	(exp (* a x))
78.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify51.0ms

Counts

63 → 63

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	124	288
1	393	252
2	1466	251
3	5002	248
done	5002	248

prune156.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* a x)))
0.0b	(exp (* 1/2 (* a x)))
0.0b	(exp (* a x))
3.9b	(fma (sqrt (exp (* a x))) (exp (* 1/2 (* a x))) (- 1.0))

rewrite17.0ms

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:

3.0ms	(sqrt (exp (* a x)))
8.0ms	(exp (* 1/2 (* a x)))
4.0ms	(exp (* a x))
0.0ms	(fma (sqrt (exp (* a x))) (exp (* 1/2 (* a x))) (- 1.0))

series147.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (exp (* a x)))
20.0ms	(exp (* 1/2 (* a x)))
14.0ms	(exp (* a x))
85.0ms	(fma (sqrt (exp (* a x))) (exp (* 1/2 (* a x))) (- 1.0))

simplify64.0ms

Counts

63 → 63

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	140	318
1	459	289
2	1755	282
3	5002	264
done	5002	264

prune169.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize13.0ms

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 (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp (* 1/2 (* a x))) (- 1.0))

rewrite8.0ms

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 (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp (* 1/2 (* a x))) (- 1.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt (exp (* a x)))
51.0ms	(cbrt (exp (* a x)))
45.0ms	(cbrt (exp (* a x)))
88.0ms	(fma (sqrt (* (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))))) (exp (* 1/2 (* a x))) (- 1.0))

simplify43.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	119	509
1	337	453
2	1250	438
3	5001	409
done	5001	409

prune204.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

regimes234.0ms

Accuracy

94.4% (1.2b remaining)

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

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	50	30
done	50	30

end0.0ms

sample933.0ms

Algorithm

intervals

Results

415.0ms	2729×	body	1280	valid
120.0ms	1269×	body	640	valid
95.0ms	5473×	body	80	valid
50.0ms	792×	body	320	valid
16.0ms	398×	body	160	valid