Details

sample154.0ms

Algorithm

intervals

Results

80.0ms	86×	body	10240	exit
49.0ms	283×	body	80	valid
2.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
2.0ms	5×	body	320	valid
1.0ms	2×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	24
3	24
2	20
1	13
0	8

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.5b	(log1p (exp x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-neg` `prod-diff`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 32

Calls

2 calls:

4.0ms	(- (log1p (exp x)) (* y x))
0.0ms	(log1p (exp x))

series139.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (log1p (exp x)) (* y x))
70.0ms	(log1p (exp x))

simplify1.5s

Counts

38 → 38

Iterations

Iter	Nodes
4	2314
3	889
2	310
1	124
0	59

prune231.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `fma-neg` `prod-diff` `add-cube-cbrt` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `associate--l+` `add-exp-log` `fma-udef` `log1p-expm1-u` `flip--`

Counts

1 → 21

Calls

1 calls:

4.0ms

(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

simplify8.7s

Counts

24 → 24

Iterations

Iter	Nodes
4	9186
3	1745
2	347
1	123
0	52

prune214.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (exp x))
0.0b	(/ (+ 1 (exp x)) (exp (* y x)))
0.1b	(exp (* y x))
2.0b	(log (/ (+ 1 (exp x)) (exp (* y x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
8×	`distribute-lft-out` `add-log-exp`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-def`
2×	`flip3-+` `div-exp` `rem-log-exp` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `log-div` `exp-prod` `clear-num` `sum-log` `frac-2neg` `exp-to-pow` `log-pow` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

9.0ms	(+ 1 (exp x))
38.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
7.0ms	(exp (* y x))
7.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1 (exp x))
35.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
13.0ms	(exp (* y x))
50.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))

simplify8.2s

Counts

105 → 105

Iterations

Iter	Nodes
4	6025
3	1784
2	665
1	292
0	130

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* y x)))
0.2b	(sqrt (exp (* y x)))
1.7b	(log (/ (+ 1 (exp x)) (sqrt (exp (* y x)))))
4.9b	(log (/ 1 (sqrt (exp (* y x)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

50×	`log-prod`
46×	`*-un-lft-identity`
42×	`times-frac`
36×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
27×	`sqrt-prod`
12×	`add-exp-log`
10×	`pow1`
9×	`sqrt-pow1`
8×	`log-pow`
7×	`add-log-exp`
6×	`rem-log-exp` `distribute-lft-out`
5×	`pow-flip`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `exp-to-pow` `pow1/2` `div-exp`
2×	`rem-sqrt-square` `log-div` `div-inv`
1×	`rec-exp` `1-exp` `log-rec` `inv-pow`

Counts

4 → 119

Calls

4 calls:

4.0ms	(sqrt (exp (* y x)))
3.0ms	(sqrt (exp (* y x)))
6.0ms	(log (/ (+ 1 (exp x)) (sqrt (exp (* y x)))))
4.0ms	(log (/ 1 (sqrt (exp (* y x)))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* y x)))
36.0ms	(sqrt (exp (* y x)))
91.0ms	(log (/ (+ 1 (exp x)) (sqrt (exp (* y x)))))
63.0ms	(log (/ 1 (sqrt (exp (* y x)))))

simplify2.1s

Counts

131 → 131

Iterations

Iter	Nodes
4	2518
3	1194
2	574
1	327
0	182

prune1.4s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.0s	2421×	body	10240	exit
1.1s	8428×	body	80	valid
143.0ms	251×	body	640	valid
109.0ms	132×	body	1280	valid
65.0ms	201×	body	320	valid
21.0ms	111×	body	160	valid