Details

sample86.0ms

Algorithm

intervals

Results

35.0ms	85×	body	1280	valid
21.0ms	39×	body	640	valid
11.0ms	182×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	14×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2061
8	2061
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.8b	(- (exp (* a x)) 1)

rewrite32.0ms

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:

8.0ms	(exp (* a x))
23.0ms	(- (exp (* a x)) 1)

series83.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(exp (* a x))
58.0ms	(- (exp (* a x)) 1)

simplify1.2s

Counts

34 → 34

Iterations

Iter	Nodes
done	2009
4	2009
3	1134
2	328
1	123
0	56

prune346.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (* a x) (* a x)) a)
4.0b	(* (* 1/6 x) (* (* (* a x) (* a x)) a))
5.0b	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
11.8b	(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

rewrite876.0ms

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:

86.0ms	(* (* (* a x) (* a x)) a)
261.0ms	(* (* 1/6 x) (* (* (* a x) (* a x)) a))
72.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
454.0ms	(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* (* a x) (* a x)) a)
111.0ms	(* (* 1/6 x) (* (* (* a x) (* a x)) a))
71.0ms	(+ (* 1/2 (* (* a x) (* a x))) (* a x))
130.0ms	(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))

simplify1.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	2005
2	2005
1	515
0	155

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (* 3 a)))
0.0b	(/ (+ -1 (exp (* x (* 3 a)))) (+ (* (exp (* a x)) (+ 1 (exp (* a x)))) 1))
0.2b	(* x (* 3 a))
3.7b	(+ -1 (exp (* x (* 3 a))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
8×	`add-log-exp`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `flip3-+` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `exp-prod` `clear-num` `sum-log` `frac-2neg` `exp-to-pow` `div-exp` `associate-r` `*-commutative` `div-inv` `rem-exp-log`

Counts

4 → 79

Calls

4 calls:

12.0ms	(exp (* x (* 3 a)))
51.0ms	(/ (+ -1 (exp (* x (* 3 a)))) (+ (* (exp (* a x)) (+ 1 (exp (* a x)))) 1))
13.0ms	(* x (* 3 a))
9.0ms	(+ -1 (exp (* x (* 3 a))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (* x (* 3 a)))
98.0ms	(/ (+ -1 (exp (* x (* 3 a)))) (+ (* (exp (* a x)) (+ 1 (exp (* a x)))) 1))
29.0ms	(* x (* 3 a))
52.0ms	(+ -1 (exp (* x (* 3 a))))

simplify1.4s

Counts

91 → 91

Iterations

Iter	Nodes
done	2041
3	2041
2	1403
1	380
0	149

prune916.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 3 (* a x)))
0.0b	(/ (- (exp (* 3 (* a x))) 1) (+ (* (exp (* a x)) (+ 1 (exp (* a x)))) 1))
0.2b	(* 3 (* a x))
3.7b	(- (exp (* 3 (* a x))) 1)

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`difference-of-squares`
9×	`pow1`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
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 → 96

Calls

4 calls:

15.0ms	(exp (* 3 (* a x)))
83.0ms	(/ (- (exp (* 3 (* a x))) 1) (+ (* (exp (* a x)) (+ 1 (exp (* a x)))) 1))
26.0ms	(* 3 (* a x))
25.0ms	(- (exp (* 3 (* a x))) 1)

series240.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (* 3 (* a x)))
114.0ms	(/ (- (exp (* 3 (* a x))) 1) (+ (* (exp (* a x)) (+ 1 (exp (* a x)))) 1))
33.0ms	(* 3 (* a x))
72.0ms	(- (exp (* 3 (* a x))) 1)

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	2019
3	2019
2	1286
1	411
0	163

prune1.1s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes362.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.5b

bsearch1.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	38
1	38
0	25

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	2653×	body	1280	valid
462.0ms	1332×	body	640	valid
343.0ms	5488×	body	80	valid
141.0ms	758×	body	320	valid
74.0ms	393×	body	160	valid