Details

sample45.0ms

Algorithm

intervals

Results

14.0ms	81×	body	1280	valid
9.0ms	47×	body	640	valid
4.0ms	163×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	16×	body	160	valid

simplify3.1s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.6b	(- (exp (* a x)) 1.0)

rewrite33.0ms

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` `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 → 40

Calls

2 calls:

9.0ms	(exp (* a x))
22.0ms	(- (exp (* a x)) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
61.0ms	(- (exp (* a x)) 1.0)

simplify1.7s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
3	1456
2	412
1	182
0	79

prune232.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
4.4b	(fma 1/2 (* (* a x) (* a x)) (* x a))
12.1b	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* x a)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

4 → 92

Calls

4 calls:

32.0ms	(* (* a x) (* a x))
21.0ms	(* (* a x) (* a x))
1.0ms	(fma 1/2 (* (* a x) (* a x)) (* x a))
1.0ms	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* x a)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* a x) (* a x))
47.0ms	(* (* a x) (* a x))
116.0ms	(fma 1/2 (* (* a x) (* a x)) (* x a))
156.0ms	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* x a)))

simplify3.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	4094
2	681
1	176
0	75

prune432.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x a))
0.0b	(exp (* x a))
0.2b	(* x (fma 2 a a))
4.5b	(- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(exp (* x a))
3.0ms	(exp (* x a))
5.0ms	(* x (fma 2 a a))
21.0ms	(- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0))

series200.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (* x a))
25.0ms	(exp (* x a))
54.0ms	(* x (fma 2 a a))
97.0ms	(- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0))

simplify2.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
3	3394
2	719
1	259
0	110

prune535.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize147.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) x)
0.2b	(* (* 3 a) x)
0.2b	(* 3 (* (* 3 a) x))
4.4b	(- (exp (* 3 (* (* 3 a) x))) (* (* (* (* 1.0 1.0) (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) 1.0))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 83

Calls

4 calls:

13.0ms	(* (* 3 a) x)
22.0ms	(* (* 3 a) x)
42.0ms	(* 3 (* (* 3 a) x))
33.0ms	(- (exp (* 3 (* (* 3 a) x))) (* (* (* (* 1.0 1.0) (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) 1.0))

series173.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3 a) x)
35.0ms	(* (* 3 a) x)
35.0ms	(* 3 (* (* 3 a) x))
80.0ms	(- (exp (* 3 (* (* 3 a) x))) (* (* (* (* 1.0 1.0) (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) 1.0))

simplify1.5s

Counts

95 → 95

Iterations

Iter	Nodes
done	5002
2	1160
1	320
0	118

prune736.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes142.0ms

Accuracy

37.4% (13.9b remaining)

Error of 14.0b against oracle of 0.1b and baseline of 22.3b

bsearch431.0ms

Steps

Iters	Range		Point
9	1.4933560481619722e+96	2.1498767242488486e+105	1.61596322380751e+101
5	-2.639018161482553e-43	-8.703467406804623e-44	-2.2530088269998953e-43
9	-1.5217483354069433e-28	-2.593318257876323e-34	-2.7735030981717545e-34
9	-1.2225730314059041e+79	-1.8599689544989674e+74	-4.7697460024798494e+75

simplify60.0ms

Iterations

Iter	Nodes
done	78
1	78
0	62

end0.0ms

sample2.2s

Algorithm

intervals

Results

832.0ms	2713×	body	1280	valid
700.0ms	5565×	body	80	valid
268.0ms	1249×	body	640	valid
124.0ms	749×	body	320	valid
29.0ms	361×	body	160	valid