Details

sample45.0ms

Algorithm

intervals

Results

16.0ms	82×	body	1280	valid
6.0ms	45×	body	640	valid
5.0ms	165×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	11×	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: 27.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.6b	(- (exp (* a x)) 1.0)

rewrite18.0ms

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:

3.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series71.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
57.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

46 → 46

Iterations

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

prune202.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
5.0b	(fma 1/2 (* (* a x) (* a x)) (* x a))
12.6b	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* x a)))

rewrite54.0ms

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:

25.0ms	(* (* a x) (* a x))
24.0ms	(* (* a x) (* a x))
0.0ms	(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)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* a x) (* a x))
36.0ms	(* (* a x) (* a x))
103.0ms	(fma 1/2 (* (* a x) (* a x)) (* x a))
166.0ms	(fma 1/6 (* (* a x) (* (* a x) (* a x))) (fma 1/2 (* (* a x) (* a x)) (* x a)))

simplify3.5s

Counts

104 → 104

Iterations

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

prune460.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x a))
0.2b	(* x (fma 2 a a))
0.2b	(/ (- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0)) (fma (exp (* x a)) (exp (* x a)) (* 1.0 (+ 1.0 (exp (* x a))))))
2.6b	(- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `fma-udef`
5×	`fma-neg` `prod-diff`
4×	`expm1-log1p-u` `exp-sum` `log1p-expm1-u`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `associate-r` `associate-l` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `exp-prod` `clear-num` `sub-neg` `frac-2neg` `exp-to-pow` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

4.0ms	(exp (* x a))
6.0ms	(* x (fma 2 a a))
46.0ms	(/ (- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0)) (fma (exp (* x a)) (exp (* x a)) (* 1.0 (+ 1.0 (exp (* x a))))))
14.0ms	(- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (* x a))
54.0ms	(* x (fma 2 a a))
188.0ms	(/ (- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0)) (fma (exp (* x a)) (exp (* x a)) (* 1.0 (+ 1.0 (exp (* x a))))))
70.0ms	(- (exp (* x (fma 2 a a))) (* (* 1.0 1.0) 1.0))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1259
1	420
0	171

prune674.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* 3 a))
0.2b	(/ (log (exp (- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0)))) (fma (exp (* x a)) (exp (* x a)) (* 1.0 (+ 1.0 (exp (* x a))))))
2.6b	(log (exp (- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0))))
2.6b	(- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
20×	`log-pow`
15×	`exp-prod`
14×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
8×	`log-prod`
7×	`associate-/l*`
6×	`prod-diff` `add-log-exp`
5×	`exp-sum`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-div` `sub-neg` `exp-diff`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `diff-log` `div-sub` `div-exp` `rem-log-exp` `associate-r` `*-commutative` `div-inv` `flip--`

Counts

4 → 109

Calls

4 calls:

12.0ms	(* x (* 3 a))
150.0ms	(/ (log (exp (- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0)))) (fma (exp (* x a)) (exp (* x a)) (* 1.0 (+ 1.0 (exp (* x a))))))
47.0ms	(log (exp (- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0))))
21.0ms	(- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0))

series353.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* x (* 3 a))
188.0ms	(/ (log (exp (- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0)))) (fma (exp (* x a)) (exp (* x a)) (* 1.0 (+ 1.0 (exp (* x a))))))
80.0ms	(log (exp (- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0))))
52.0ms	(- (exp (* x (* 3 a))) (* (* 1.0 1.0) 1.0))

simplify3.0s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
3	4506
2	1306
1	442
0	209

prune782.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes376.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.5b

bsearch2.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample1.8s

Algorithm

intervals

Results

811.0ms	2696×	body	1280	valid
281.0ms	1292×	body	640	valid
228.0ms	5427×	body	80	valid
84.0ms	757×	body	320	valid
30.0ms	410×	body	160	valid