Details

sample128.0ms

Algorithm

intervals

Results

70.0ms	62×	body	10240	exit
30.0ms	259×	body	80	valid
6.0ms	8×	body	640	valid
4.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	3×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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:

5.0ms	(- (log1p (exp x)) (* y x))
0.0ms	(log1p (exp x))

series146.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(- (log1p (exp x)) (* y x))
71.0ms	(log1p (exp x))

simplify4.0s

Counts

40 → 40

Iterations

Iter	Nodes
done	5020
4	3846
3	1021
2	320
1	128
0	61

prune227.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

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))

rewrite13.0ms

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:

12.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
0.0ms	(fma x (fma x 1/8 1/2) (log 2))

series138.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
52.0ms	(fma x (fma x 1/8 1/2) (log 2))

simplify2.4s

Counts

39 → 39

Iterations

Iter	Nodes
done	5001
3	1868
2	369
1	132
0	59

prune203.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (* (exp (* x (fma 1/8 x 1/2))) 2)) (* y x))
0.0b	(* x (fma 1/8 x 1/2))
0.5b	(log (* (exp (* x (fma 1/8 x 1/2))) 2))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
6×	`log-pow`
5×	`add-cbrt-cube` `fma-neg` `prod-diff`
4×	`pow-prod-down` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
2×	`log-prod` `rem-log-exp` `prod-exp` `fma-udef`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

50.0ms	(- (log (* (exp (* x (fma 1/8 x 1/2))) 2)) (* y x))
6.0ms	(* x (fma 1/8 x 1/2))
17.0ms	(log (* (exp (* x (fma 1/8 x 1/2))) 2))

series312.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(- (log (* (exp (* x (fma 1/8 x 1/2))) 2)) (* y x))
91.0ms	(* x (fma 1/8 x 1/2))
110.0ms	(log (* (exp (* x (fma 1/8 x 1/2))) 2))

simplify2.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	3566
2	640
1	241
0	103

prune296.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (exp x))
0.0b	(exp (* y x))
0.3b	(/ (+ 1 (exp x)) (exp (* y x)))
1.8b	(log (/ (+ 1 (exp x)) (exp (* y x))))

rewrite41.0ms

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` `insert-posit16` `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 → 97

Calls

4 calls:

5.0ms	(+ 1 (exp x))
4.0ms	(exp (* y x))
24.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
6.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ 1 (exp x))
20.0ms	(exp (* y x))
42.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
54.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))

simplify2.2s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
3	2296
2	722
1	301
0	134

prune401.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes68.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	7
1	7
0	6

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.3s	2288×	body	10240	exit
754.0ms	8318×	body	80	valid
128.0ms	262×	body	640	valid
117.0ms	147×	body	1280	valid
56.0ms	186×	body	320	valid
22.0ms	108×	body	160	valid