Details

sample66.0ms

Algorithm

intervals

Results

25.0ms	82×	body	1280	valid
10.0ms	45×	body	640	valid
7.0ms	165×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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))
19.0ms	(- (exp (* a x)) 1.0)

series74.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(exp (* a x))
57.0ms	(- (exp (* a x)) 1.0)

simplify1.5s

Counts

30 → 30

Iterations

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

prune161.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.6b	(* (* 1/6 a) (* (* x a) (* x a)))
1.4b	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
12.6b	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

rewrite582.0ms

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:

5.0ms	(* 1/6 a)
107.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
352.0ms	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
114.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/6 a)
82.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
168.0ms	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
121.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

simplify2.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3138
1	502
0	152

prune536.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.6b	(* (* 1/6 a) (* (* x a) (* x a)))
4.1b	(* x (* (* 1/6 a) (* (* x a) (* x a))))
12.6b	(+ (* (* (* x a) (* x a)) 1/2) (+ (* x (* (* 1/6 a) (* (* x a) (* x a)))) (* x a)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

100×	`pow1` `add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

11.0ms	(* 1/6 a)
95.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
285.0ms	(* x (* (* 1/6 a) (* (* x a) (* x a))))
700.0ms	(+ (* (* (* x a) (* x a)) 1/2) (+ (* x (* (* 1/6 a) (* (* x a) (* x a)))) (* x a)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 1/6 a)
74.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
110.0ms	(* x (* (* 1/6 a) (* (* x a) (* x a))))
153.0ms	(+ (* (* (* x a) (* x a)) 1/2) (+ (* x (* (* 1/6 a) (* (* x a) (* x a)))) (* x a)))

simplify2.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5002
2	3438
1	542
0	160

prune413.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x a))
0.2b	(* 3 (* x a))
0.2b	(/ (- (exp (* 3 (* x a))) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp (* x a)) (+ (exp (* x a)) 1.0))))
2.6b	(- (exp (* 3 (* x a))) (* (* 1.0 1.0) 1.0))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `times-frac`
8×	`add-log-exp`
3×	`associate-/r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `exp-prod` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `exp-to-pow` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 72

Calls

4 calls:

6.0ms	(exp (* x a))
24.0ms	(* 3 (* x a))
73.0ms	(/ (- (exp (* 3 (* x a))) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp (* x a)) (+ (exp (* x a)) 1.0))))
38.0ms	(- (exp (* 3 (* x a))) (* (* 1.0 1.0) 1.0))

series254.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (* x a))
31.0ms	(* 3 (* x a))
145.0ms	(/ (- (exp (* 3 (* x a))) (* (* 1.0 1.0) 1.0)) (+ (* 1.0 1.0) (* (exp (* x a)) (+ (exp (* x a)) 1.0))))
60.0ms	(- (exp (* 3 (* x a))) (* (* 1.0 1.0) 1.0))

simplify1.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	2032
1	435
0	158

prune449.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes317.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	33
3	33
2	31
1	28
0	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

802.0ms	2696×	body	1280	valid
323.0ms	1292×	body	640	valid
302.0ms	5427×	body	80	valid
91.0ms	757×	body	320	valid
80.0ms	410×	body	160	valid