Details

sample116.0ms

Algorithm

intervals

Results

70.0ms	86×	body	10240	exit
20.0ms	261×	body	80	valid
6.0ms	11×	body	640	valid
5.0ms	7×	body	1280	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	26
3	26
2	22
1	15
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 34

Calls

2 calls:

10.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series161.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(- (log1p (exp x)) (* y x))
82.0ms	(log1p (exp x))

simplify1.3s

Counts

40 → 40

Iterations

Iter	Nodes
done	2002
4	2002
3	1021
2	320
1	128
0	61

prune150.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (- (log1p (exp x)) (* y x)))
0.0b	(- (log1p (exp x)) (* y x))
0.5b	(log1p (exp x))
1.2b	(expm1 (log1p (- (log1p (exp x)) (* y x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`log1p-udef` `fma-neg` `prod-diff`
2×	`diff-log` `log1p-expm1`
1×	`expm1-log1p` `sub-neg` `flip3--` `flip--` `expm1-udef`

Counts

4 → 58

Calls

4 calls:

1.0ms	(log1p (- (log1p (exp x)) (* y x)))
17.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))
1.0ms	(expm1 (log1p (- (log1p (exp x)) (* y x))))

series798.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(log1p (- (log1p (exp x)) (* y x)))
70.0ms	(- (log1p (exp x)) (* y x))
85.0ms	(log1p (exp x))
394.0ms	(expm1 (log1p (- (log1p (exp x)) (* y x))))

simplify1.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	2006
3	2006
2	1225
1	386
0	152

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 33

Calls

2 calls:

11.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
1.0ms	(fma x (fma x 1/8 1/2) (log 2))

series98.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
39.0ms	(fma x (fma x 1/8 1/2) (log 2))

simplify1.4s

Counts

39 → 39

Iterations

Iter	Nodes
done	2003
4	2003
3	1868
2	369
1	132
0	59

prune266.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (exp x))
0.7b	(* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x))))
1.2b	(expm1 (cbrt (* (* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x)))) (log1p (- (log1p (exp x)) (* y x))))))
3.5b	(cbrt (* (* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x)))) (log1p (- (log1p (exp x)) (* y x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`insert-posit16` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
1×	`cbrt-prod` `pow2` `log1p-udef` `expm1-log1p` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `prod-exp` `log1p-expm1` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

0.0ms	(log1p (exp x))
6.0ms	(* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x))))
0.0ms	(expm1 (cbrt (* (* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x)))) (log1p (- (log1p (exp x)) (* y x))))))
15.0ms	(cbrt (* (* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x)))) (log1p (- (log1p (exp x)) (* y x)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

87.0ms	(log1p (exp x))
711.0ms	(* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x))))
344.0ms	(expm1 (cbrt (* (* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x)))) (log1p (- (log1p (exp x)) (* y x))))))
250.0ms	(cbrt (* (* (log1p (- (log1p (exp x)) (* y x))) (log1p (- (log1p (exp x)) (* y x)))) (log1p (- (log1p (exp x)) (* y x)))))

simplify1.9s

Counts

77 → 77

Iterations

Iter	Nodes
done	2002
2	2002
1	910
0	279

prune480.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes104.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	7
1	7
0	6

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.1s	2261×	body	10240	exit
833.0ms	8357×	body	80	valid
170.0ms	323×	body	640	valid
91.0ms	116×	body	1280	valid
55.0ms	195×	body	320	valid
43.0ms	95×	body	160	valid