Details

sample80.0ms

Algorithm

intervals

Results

36.0ms	90×	body	1280	valid
8.0ms	39×	body	640	valid
7.0ms	163×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3485
6	450
5	118
4	51
3	27
2	18
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (exp (* a x)) 1.0)

rewrite32.0ms

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))
20.0ms	(- (exp (* a x)) 1.0)

series63.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(exp (* a x))
41.0ms	(- (exp (* a x)) 1.0)

simplify2.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
3	3404
2	600
1	183
0	79

prune294.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 a)
0.8b	(* (* 1/6 a) (* (* x a) (* x a)))
1.5b	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
11.8b	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1` `add-cbrt-cube` `add-exp-log`
33×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef`

Counts

4 → 96

Calls

4 calls:

11.0ms	(* 1/6 a)
127.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
24.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
1.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/6 a)
59.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
162.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
165.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	2797
1	447
0	147

prune530.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(* a 1/6)
1.4b	(* x (* (* x a) (* x a)))
3.2b	(* (* x (* (* x a) (* x a))) (* a 1/6))
11.8b	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* (* x (* (* x a) (* x a))) (* a 1/6))))

rewrite756.0ms

Algorithm

rewrite-expression-head

Rules

80×	`pow1` `add-cbrt-cube` `add-exp-log`
58×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`fma-udef`

Counts

4 → 108

Calls

4 calls:

11.0ms	(* a 1/6)
104.0ms	(* x (* (* x a) (* x a)))
631.0ms	(* (* x (* (* x a) (* x a))) (* a 1/6))
1.0ms	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* (* x (* (* x a) (* x a))) (* a 1/6))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* a 1/6)
46.0ms	(* x (* (* x a) (* x a)))
86.0ms	(* (* x (* (* x a) (* x a))) (* a 1/6))
144.0ms	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* (* x (* (* x a) (* x a))) (* a 1/6))))

simplify2.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2718
1	430
0	144

prune496.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.2b	(* 3 (* a x))
3.8b	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

3.0ms	(exp (* a x))
3.0ms	(exp (* a x))
12.0ms	(* 3 (* a x))
25.0ms	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

series142.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* a x))
23.0ms	(exp (* a x))
35.0ms	(* 3 (* a x))
61.0ms	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1217
1	255
0	103

prune548.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes550.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.5b

bsearch2.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	43
3	43
2	41
1	38
0	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

975.0ms	2701×	body	1280	valid
294.0ms	1304×	body	640	valid
259.0ms	5509×	body	80	valid
121.0ms	804×	body	320	valid
33.0ms	387×	body	160	valid