Details

sample50.0ms

Algorithm

intervals

Results

21.0ms	83×	body	1280	valid
7.0ms	53×	body	640	valid
5.0ms	169×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	3255
6	440
5	113
4	49
3	26
2	18
1	11
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (exp (* a x)) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 24

Calls

2 calls:

6.0ms	(exp (* a x))
22.0ms	(- (exp (* a x)) 1.0)

series75.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(exp (* a x))
60.0ms	(- (exp (* a x)) 1.0)

simplify1.4s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
3	2000
2	389
1	116
0	53

prune120.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
1.4b	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
1.8b	(* (* 1/6 a) (* (* x a) (* x a)))
12.1b	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

rewrite512.0ms

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`
6×	`add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

4 → 93

Calls

4 calls:

6.0ms	(* 1/6 a)
295.0ms	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
114.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
90.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 1/6 a)
187.0ms	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
59.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
146.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

simplify2.7s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3133
1	504
0	152

prune538.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize106.0ms

Local error

Found 4 expressions with local error:

12.1b	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))
17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
3×	`pow1/3`
2×	`associate-+r+`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`

Counts

4 → 52

Calls

4 calls:

78.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))
118.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
117.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
117.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

176.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))
376.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
385.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
326.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))

simplify2.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1392
1	299
0	110

prune602.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize188.0ms

Local error

Found 4 expressions with local error:

17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
17.5b	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

95.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
75.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
119.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
105.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))

series1.5s

Counts

4 → 12

Calls

4 calls:

366.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
386.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
361.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))
361.0ms	(cbrt (+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))))

simplify1.9s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1057
1	241
0	91

prune499.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

36.6% (13.5b remaining)

Error of 13.6b against oracle of 0.1b and baseline of 21.4b

bsearch117.0ms

Steps

Iters	Range		Point
6	1.002525777773014e+61	7.978302556291104e+61	2.4322510983861363e+61
9	-4.216905555238471e+117	-5.732665707936787e+112	-1.7687231827076556e+113

simplify7.0ms

Iterations

Iter	Nodes
done	45
1	45
0	30

end0.0ms

sample1.8s

Algorithm

intervals

Results

775.0ms	2738×	body	1280	valid
265.0ms	5502×	body	80	valid
219.0ms	1280×	body	640	valid
155.0ms	757×	body	320	valid
92.0ms	393×	body	160	valid