Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	76×	body	1280	valid
11.0ms	74×	body	10240	exit
7.0ms	46×	body	640	valid
3.0ms	100×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 51

Calls

2 calls:

16.0ms	(/ (exp x) (- (exp x) 1.0))
9.0ms	(- (exp x) 1.0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (exp x) (- (exp x) 1.0))
32.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	1479
2	540
1	191
0	91

prune221.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.2b	(* 1/12 x)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

62.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
6.0ms	(* 1/12 x)

series37.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
20.0ms	(* 1/12 x)

simplify1.9s

Counts

37 → 37

Iterations

Iter	Nodes
done	5002
3	1810
2	477
1	154
0	58

prune154.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (/ (- (* (exp x) (* (exp x) (exp x))) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))))
0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
3.5b	(- (* (exp x) (* (exp x) (exp x))) (* (* 1.0 1.0) 1.0))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
79×	`add-sqr-sqrt`
75×	`*-un-lft-identity` `add-cube-cbrt`
36×	`exp-prod`
18×	`pow1` `associate-/r*`
13×	`difference-cubes` `add-cbrt-cube` `cube-unmult` `pow3`
9×	`associate-/r/`
8×	`pow-prod-down` `pow-sqr` `pow-prod-up`
7×	`add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`div-inv`
4×	`flip3-+` `flip-+`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--`

Counts

4 → 171

Calls

4 calls:

183.0ms	(/ (exp x) (/ (- (* (exp x) (* (exp x) (exp x))) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))))
28.0ms	(* (exp x) (exp x))
28.0ms	(* (exp x) (exp x))
76.0ms	(- (* (exp x) (* (exp x) (exp x))) (* (* 1.0 1.0) 1.0))

series254.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (exp x) (/ (- (* (exp x) (* (exp x) (exp x))) (* (* 1.0 1.0) 1.0)) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))))
25.0ms	(* (exp x) (exp x))
24.0ms	(* (exp x) (exp x))
59.0ms	(- (* (exp x) (* (exp x) (exp x))) (* (* 1.0 1.0) 1.0))

simplify2.6s

Counts

183 → 183

Iterations

Iter	Nodes
done	5026
2	3020
1	795
0	283

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (/ (- (* (exp x) (* (exp x) (exp x))) 1.0) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))))
0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
3.5b	(- (* (exp x) (* (exp x) (exp x))) 1.0)

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
72×	`add-sqr-sqrt`
68×	`*-un-lft-identity` `add-cube-cbrt`
36×	`exp-prod`
18×	`pow1`
15×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`associate-/r/`
8×	`pow-prod-down` `pow-sqr` `pow-prod-up`
7×	`add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`div-inv`
4×	`flip3-+` `flip-+`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--`

Counts

4 → 158

Calls

4 calls:

163.0ms	(/ (exp x) (/ (- (* (exp x) (* (exp x) (exp x))) 1.0) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))))
15.0ms	(* (exp x) (exp x))
17.0ms	(* (exp x) (exp x))
62.0ms	(- (* (exp x) (* (exp x) (exp x))) 1.0)

series280.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (exp x) (/ (- (* (exp x) (* (exp x) (exp x))) 1.0) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0)))))
30.0ms	(* (exp x) (exp x))
24.0ms	(* (exp x) (exp x))
47.0ms	(- (* (exp x) (* (exp x) (exp x))) 1.0)

simplify2.6s

Counts

170 → 170

Iterations

Iter	Nodes
done	5003
2	2784
1	697
0	253

prune930.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes110.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.5b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2638×	body	10240	exit
642.0ms	2240×	body	1280	valid
381.0ms	1645×	body	640	valid
127.0ms	2866×	body	80	valid
125.0ms	828×	body	320	valid
30.0ms	421×	body	160	valid