Details

sample86.0ms

Algorithm

intervals

Results

24.0ms	96×	body	10240	exit
22.0ms	64×	body	1280	valid
14.0ms	61×	body	640	valid
5.0ms	104×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
3.2b	(- (exp x) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

37.0ms	(/ (exp x) (- (exp x) 1.0))
25.0ms	(- (exp x) 1.0)

series172.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(/ (exp x) (- (exp x) 1.0))
69.0ms	(- (exp x) 1.0)

simplify3.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5028
3	2064
2	672
1	253
0	117

prune431.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1 x) (fma 1/12 x 1/2))
0.1b	(fma 1/12 x 1/2)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

13×	`fma-def`
12×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
4×	`add-log-exp`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `div-inv` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `sum-log` `flip-+`

Counts

2 → 39

Calls

2 calls:

38.0ms	(+ (/ 1 x) (fma 1/12 x 1/2))
1.0ms	(fma 1/12 x 1/2)

series105.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (/ 1 x) (fma 1/12 x 1/2))
79.0ms	(fma 1/12 x 1/2)

simplify3.5s

Counts

45 → 45

Iterations

Iter	Nodes
done	5002
3	1939
2	470
1	114
0	42

prune405.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (fma 1/12 x 1/2))
0.0b	(+ (/ 1 x) (expm1 (log1p (fma 1/12 x 1/2))))
0.0b	(expm1 (log1p (fma 1/12 x 1/2)))
0.1b	(fma 1/12 x 1/2)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`fma-def`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
2×	`div-inv` `distribute-lft-out` `expm1-udef`
1×	`+-commutative` `associate-+r-` `log1p-udef` `expm1-log1p` `flip3-+` `log1p-expm1` `sum-log` `flip-+` `fma-udef`

Counts

4 → 61

Calls

4 calls:

1.0ms	(log1p (fma 1/12 x 1/2))
46.0ms	(+ (/ 1 x) (expm1 (log1p (fma 1/12 x 1/2))))
0.0ms	(expm1 (log1p (fma 1/12 x 1/2)))
1.0ms	(fma 1/12 x 1/2)

series1.5s

Counts

4 → 12

Calls

4 calls:

55.0ms	(log1p (fma 1/12 x 1/2))
597.0ms	(+ (/ 1 x) (expm1 (log1p (fma 1/12 x 1/2))))
808.0ms	(expm1 (log1p (fma 1/12 x 1/2)))
65.0ms	(fma 1/12 x 1/2)

simplify6.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	3135
2	819
1	256
0	107

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize100.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (log1p (fma 1/12 x 1/2))))
0.0b	(expm1 (expm1 (log1p (log1p (fma 1/12 x 1/2)))))
0.1b	(fma 1/12 x 1/2)
0.6b	(log1p (log1p (fma 1/12 x 1/2)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

1.0ms	(expm1 (log1p (log1p (fma 1/12 x 1/2))))
1.0ms	(expm1 (expm1 (log1p (log1p (fma 1/12 x 1/2)))))
1.0ms	(fma 1/12 x 1/2)
3.0ms	(log1p (log1p (fma 1/12 x 1/2)))

series10.3s

Counts

4 → 12

Calls

4 calls:

238.0ms	(expm1 (log1p (log1p (fma 1/12 x 1/2))))
9.2s	(expm1 (expm1 (log1p (log1p (fma 1/12 x 1/2)))))
146.0ms	(fma 1/12 x 1/2)
705.0ms	(log1p (log1p (fma 1/12 x 1/2)))

simplify7.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
3	3470
2	889
1	298
0	130

prune572.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

regimes96.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 21.8b

bsearch273.0ms

Steps

Iters	Range		Point
9	-1.440408271564231	-1.963203309137196e-05	-0.0015746675324234964

simplify27.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.8s	2605×	body	10240	exit
1.3s	2280×	body	1280	valid
1.3s	2844×	body	80	valid
486.0ms	1590×	body	640	valid
131.0ms	840×	body	320	valid
44.0ms	447×	body	160	valid