Details

sample82.0ms

Algorithm

intervals

Results

40.0ms	93×	body	1280	valid
11.0ms	181×	body	80	valid
11.0ms	37×	body	640	valid
5.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (exp (* a x)) 1)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

4.0ms	(exp (* a x))
12.0ms	(- (exp (* a x)) 1)

series71.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(exp (* a x))
48.0ms	(- (exp (* a x)) 1)

simplify2.9s

Counts

34 → 34

Iterations

Iter	Nodes
done	5002
4	3726
3	1134
2	328
1	123
0	56

prune157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) (* a x))
0.3b	(* (* a x) (* a x))
2.4b	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
8.8b	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

rewrite600.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `insert-posit16`
2×	`pow2` `+-commutative` `flip3-+` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`associate-+r+`

Counts

4 → 96

Calls

4 calls:

29.0ms	(* (* a x) (* a x))
37.0ms	(* (* a x) (* a x))
70.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
462.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* a x) (* a x))
55.0ms	(* (* a x) (* a x))
88.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
137.0ms	(+ (* (* (* (* a x) (* a x)) (* a x)) 1/6) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5024
2	1414
1	297
0	95

prune296.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp (* a x))) 1) (- (sqrt (exp (* a x))) 1))
0.0b	(exp (* a x))
0.0b	(exp (* a x))
3.4b	(- (sqrt (exp (* a x))) 1)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
11×	`associate-r`
10×	`add-log-exp`
9×	`sqrt-prod`
8×	`difference-of-squares`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-l`
4×	`frac-times` `flip3--` `difference-of-sqr-1` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `exp-prod` `distribute-lft-in` `exp-to-pow` `associate-l/` `associate-r/` `distribute-lft-out` `rem-exp-log`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

80.0ms	(* (+ (sqrt (exp (* a x))) 1) (- (sqrt (exp (* a x))) 1))
4.0ms	(exp (* a x))
4.0ms	(exp (* a x))
17.0ms	(- (sqrt (exp (* a x))) 1)

series184.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (+ (sqrt (exp (* a x))) 1) (- (sqrt (exp (* a x))) 1))
14.0ms	(exp (* a x))
15.0ms	(exp (* a x))
64.0ms	(- (sqrt (exp (* a x))) 1)

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
3	4202
2	1360
1	317
0	113

prune399.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* (* a x) (* a x)) a)
2.4b	(+ (* (* a x) 1/2) (* (* 1/8 (* a x)) (* a x)))
3.2b	(* (* 1/48 x) (* (* (* a x) (* a x)) a))
8.8b	(+ (* (* 1/48 x) (* (* (* a x) (* a x)) a)) (+ (* (* a x) 1/2) (* (* 1/8 (* a x)) (* a x))))

rewrite732.0ms

Algorithm

rewrite-expression-head

Rules

78×	`pow1` `add-cbrt-cube` `add-exp-log`
57×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`sum-log` `associate-r` `insert-posit16`
2×	`+-commutative` `flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`associate-+r+` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

83.0ms	(* (* (* a x) (* a x)) a)
34.0ms	(+ (* (* a x) 1/2) (* (* 1/8 (* a x)) (* a x)))
255.0ms	(* (* 1/48 x) (* (* (* a x) (* a x)) a))
359.0ms	(+ (* (* 1/48 x) (* (* (* a x) (* a x)) a)) (+ (* (* a x) 1/2) (* (* 1/8 (* a x)) (* a x))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* (* a x) (* a x)) a)
87.0ms	(+ (* (* a x) 1/2) (* (* 1/8 (* a x)) (* a x)))
108.0ms	(* (* 1/48 x) (* (* (* a x) (* a x)) a))
141.0ms	(+ (* (* 1/48 x) (* (* (* a x) (* a x)) a)) (+ (* (* a x) 1/2) (* (* 1/8 (* a x)) (* a x))))

simplify2.2s

Counts

114 → 114

Iterations

Iter	Nodes
done	5002
2	2328
1	533
0	160

prune395.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

95.1% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 21.2b

bsearch1.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	43
1	43
0	28

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	2805×	body	1280	valid
764.0ms	1263×	body	640	valid
344.0ms	5339×	body	80	valid
118.0ms	715×	body	320	valid
42.0ms	381×	body	160	valid