Details

sample70.0ms

Algorithm

intervals

Results

29.0ms	81×	body	1280	valid
9.0ms	49×	body	640	valid
7.0ms	177×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.1b	(- (exp (* a x)) 1.0)

rewrite29.0ms

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:

6.0ms	(exp (* a x))
21.0ms	(- (exp (* a x)) 1.0)

series74.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
61.0ms	(- (exp (* a x)) 1.0)

simplify2.6s

Counts

46 → 46

Iterations

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

prune210.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.9b	(* (* 1/6 a) (* (* x a) (* x a)))
1.4b	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
14.3b	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite110.0ms

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:

5.0ms	(* 1/6 a)
82.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
18.0ms	(* 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))))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 1/6 a)
66.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
116.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
143.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	2797
1	447
0	147

prune557.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* 3 (* a x)))
0.2b	(* 3 (* a x))
2.3b	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

rewrite88.0ms

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:

6.0ms	(exp (* a x))
14.0ms	(exp (* 3 (* a x)))
25.0ms	(* 3 (* a x))
42.0ms	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

series159.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (* a x))
33.0ms	(exp (* 3 (* a x)))
39.0ms	(* 3 (* a x))
60.0ms	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1297
1	268
0	110

prune466.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.9b	(* a (* (* a x) (* a x)))
4.5b	(* (* a (* (* a x) (* a x))) x)
14.3b	(+ (* (* a (* (* a x) (* a x))) x) (* (* a x) (* a x)))

rewrite595.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
59×	`add-cbrt-cube` `add-exp-log`
49×	`pow-prod-down`
40×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`*-commutative`
2×	`pow-plus`
1×	`pow2` `+-commutative` `sum-log` `fma-def` `flip3-+` `swap-sqr` `flip-+` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

34.0ms	(* (* a x) (* a x))
75.0ms	(* a (* (* a x) (* a x)))
230.0ms	(* (* a (* (* a x) (* a x))) x)
251.0ms	(+ (* (* a (* (* a x) (* a x))) x) (* (* a x) (* a x)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* a x) (* a x))
44.0ms	(* a (* (* a x) (* a x)))
102.0ms	(* (* a (* (* a x) (* a x))) x)
148.0ms	(+ (* (* a (* (* a x) (* a x))) x) (* (* a x) (* a x)))

simplify2.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
2	3134
1	374
0	121

prune666.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes242.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.6b

bsearch2.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	45
2	45
1	40
0	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

829.0ms	2649×	body	1280	valid
305.0ms	5450×	body	80	valid
299.0ms	1357×	body	640	valid
95.0ms	749×	body	320	valid
79.0ms	403×	body	160	valid