Details

sample95.0ms

Algorithm

intervals

Results

37.0ms	86×	body	1280	valid
11.0ms	176×	body	80	valid
10.0ms	40×	body	640	valid
8.0ms	37×	body	320	valid
1.0ms	11×	body	160	valid

simplify6.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5090
8	2971
7	747
6	218
5	94
4	45
3	24
2	16
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize63.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
4.6b	(- (exp (* a x)) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
6×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 42

Calls

2 calls:

21.0ms	(exp (* a x))
42.0ms	(- (exp (* a x)) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(exp (* a x))
65.0ms	(- (exp (* a x)) 1.0)

simplify3.6s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	1453
2	414
1	184
0	81

prune447.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x a) (* (* x a) (* x a)))
0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* x a))
9.0b	(fma (* (* x a) (* x a)) 1/2 (fma (* (* x a) (* (* x a) (* x a))) 1/6 (* a x)))

rewrite542.0ms

Algorithm

rewrite-expression-head

Rules

210×	`pow1`
94×	`pow-prod-down`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
38×	`pow-prod-up`
16×	`pow-sqr`
8×	`pow-plus`
4×	`pow2` `add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative`
2×	`swap-sqr`
1×	`cube-unmult` `fma-udef`

Counts

4 → 151

Calls

4 calls:

323.0ms	(* (* x a) (* (* x a) (* x a)))
112.0ms	(* (* x a) (* x a))
91.0ms	(* (* x a) (* x a))
1.0ms	(fma (* (* x a) (* x a)) 1/2 (fma (* (* x a) (* (* x a) (* x a))) 1/6 (* a x)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (* x a) (* (* x a) (* x a)))
68.0ms	(* (* x a) (* x a))
61.0ms	(* (* x a) (* x a))
198.0ms	(fma (* (* x a) (* x a)) 1/2 (fma (* (* x a) (* (* x a) (* x a))) 1/6 (* a x)))

simplify3.4s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	853
1	243
0	101

prune854.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (exp (* a x)) 1.0))
0.1b	(exp (* a x))
4.5b	(log (exp (- (exp (* a x)) 1.0)))
4.6b	(- (exp (* a x)) 1.0)

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
22×	`exp-sum`
14×	`log-prod`
11×	`exp-prod` `add-log-exp`
6×	`log-pow`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`
2×	`exp-diff` `diff-log`
1×	`log-div` `flip3--` `exp-to-pow` `rem-log-exp` `flip--`

Counts

4 → 103

Calls

4 calls:

84.0ms	(exp (- (exp (* a x)) 1.0))
10.0ms	(exp (* a x))
75.0ms	(log (exp (- (exp (* a x)) 1.0)))
64.0ms	(- (exp (* a x)) 1.0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(exp (- (exp (* a x)) 1.0))
20.0ms	(exp (* a x))
67.0ms	(log (exp (- (exp (* a x)) 1.0)))
54.0ms	(- (exp (* a x)) 1.0)

simplify4.1s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
3	1778
2	582
1	270
0	143

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize206.0ms

Local error

Found 4 expressions with local error:

4.5b	(log (exp (- (exp (* a x)) 1.0)))
4.6b	(- (exp (* a x)) 1.0)
4.6b	(- (exp (* a x)) 1.0)
4.6b	(- (exp (* a x)) 1.0)

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
33×	`add-cube-cbrt`
14×	`log-prod`
11×	`exp-sum`
10×	`add-log-exp`
9×	`fma-neg`
6×	`log-pow`
5×	`pow1` `exp-prod`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 119

Calls

4 calls:

94.0ms	(log (exp (- (exp (* a x)) 1.0)))
67.0ms	(- (exp (* a x)) 1.0)
66.0ms	(- (exp (* a x)) 1.0)
39.0ms	(- (exp (* a x)) 1.0)

series292.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(log (exp (- (exp (* a x)) 1.0)))
75.0ms	(- (exp (* a x)) 1.0)
70.0ms	(- (exp (* a x)) 1.0)
74.0ms	(- (exp (* a x)) 1.0)

simplify8.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
4	4768
3	1557
2	520
1	238
0	127

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes1.2s

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.7b

bsearch2.0ms

simplify21.0ms

Iterations

Iter	Nodes
done	28
1	28
0	25

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	2560×	body	1280	valid
470.0ms	5475×	body	80	valid
385.0ms	1367×	body	640	valid
153.0ms	810×	body	320	valid
52.0ms	399×	body	160	valid