Details

sample88.0ms

Algorithm

intervals

Results

34.0ms	78×	body	1280	valid
15.0ms	51×	body	640	valid
10.0ms	169×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
3	15
2	13
1	10
0	5

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize51.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.4b	(- (exp x) 1.0)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 70

Calls

2 calls:

88.0ms	(/ (- (exp x) 1.0) x)
43.0ms	(- (exp x) 1.0)

series113.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(/ (- (exp x) 1.0) x)
23.0ms	(- (exp x) 1.0)

simplify5.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2314
2	719
1	294
0	129

prune610.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x (fma x 1/6 1/2) 1)
0.1b	(fma x 1/6 1/2)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 22

Calls

2 calls:

1.0ms	(fma x (fma x 1/6 1/2) 1)
1.0ms	(fma x 1/6 1/2)

series103.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(fma x (fma x 1/6 1/2) 1)
61.0ms	(fma x 1/6 1/2)

simplify5.7s

Counts

28 → 28

Iterations

Iter	Nodes
done	5001
4	2323
3	430
2	116
1	57
0	36

prune261.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (exp (- (exp x) 1.0))) x)
3.4b	(log (exp (- (exp x) 1.0)))
3.4b	(- (exp x) 1.0)

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`log-pow`
27×	`times-frac`
25×	`exp-prod`
18×	`prod-diff`
14×	`log-prod`
11×	`exp-sum`
9×	`associate-/l*`
8×	`pow1`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r*` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `sub-neg` `exp-diff`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `diff-log` `div-sub` `div-exp` `rem-log-exp` `div-inv` `flip--`

Counts

3 → 116

Calls

3 calls:

273.0ms	(/ (log (exp (- (exp x) 1.0))) x)
81.0ms	(log (exp (- (exp x) 1.0)))
60.0ms	(- (exp x) 1.0)

series112.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (log (exp (- (exp x) 1.0))) x)
33.0ms	(log (exp (- (exp x) 1.0)))
19.0ms	(- (exp x) 1.0)

simplify4.5s

Counts

125 → 125

Iterations

Iter	Nodes
done	5009
3	2531
2	859
1	373
0	203

prune927.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (sqrt (exp (- (exp x) 1.0))))
3.4b	(log (sqrt (exp (- (exp x) 1.0))))
3.4b	(- (exp x) 1.0)
3.4b	(- (exp x) 1.0)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff` `add-cube-cbrt`
34×	`log-prod`
28×	`sqrt-prod`
22×	`exp-sum`
16×	`log-pow`
12×	`sqrt-pow1`
10×	`exp-prod`
8×	`pow1` `add-log-exp`
6×	`fma-neg` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 132

Calls

4 calls:

80.0ms	(log (sqrt (exp (- (exp x) 1.0))))
76.0ms	(log (sqrt (exp (- (exp x) 1.0))))
33.0ms	(- (exp x) 1.0)
50.0ms	(- (exp x) 1.0)

series524.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(log (sqrt (exp (- (exp x) 1.0))))
259.0ms	(log (sqrt (exp (- (exp x) 1.0))))
29.0ms	(- (exp x) 1.0)
19.0ms	(- (exp x) 1.0)

simplify7.0s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
4	3844
3	1362
2	516
1	257
0	153

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes109.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 22.0b

bsearch23.0ms

Steps

Iters	Range		Point
4	-0.00018185218373056224	-0.00010358510568112945	-0.00017882867482842777

simplify20.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2164×	body	1280	valid
520.0ms	1661×	body	640	valid
342.0ms	5551×	body	80	valid
216.0ms	834×	body	320	valid
55.0ms	425×	body	160	valid