Details

sample303.0ms

Algorithm

intervals

Results

139.0ms	247×	body	10240	exit
30.0ms	476×	body	80	nan
15.0ms	230×	body	80	valid
5.0ms	28×	body	160	valid

simplify8.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5043
8	4148
7	1069
6	332
5	133
4	65
3	37
2	27
1	19
0	10

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/` `insert-posit16`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 127

Calls

4 calls:

73.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
85.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (exp x) 1.0)

series355.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
104.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
31.0ms	(- (exp (* 2.0 x)) 1.0)
46.0ms	(- (exp x) 1.0)

simplify5.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5002
3	3360
2	1009
1	400
0	193

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.8b	(- (exp x) 1.0)
5.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

535×	`*-un-lft-identity`
520×	`sqrt-prod`
483×	`times-frac`
437×	`add-sqr-sqrt`
150×	`difference-of-squares`
131×	`add-cube-cbrt`
104×	`distribute-lft-out`
98×	`distribute-lft-out--`
11×	`associate-/r/`
10×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square`
2×	`sub-neg` `diff-log`
1×	`+-commutative` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 322

Calls

4 calls:

173.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
22.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
20.0ms	(- (exp x) 1.0)
35.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series839.0ms

Counts

4 → 12

Calls

4 calls:

608.0ms	(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (exp x) 1.0) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))))
94.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
37.0ms	(- (exp x) 1.0)
100.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify6.5s

Counts

334 → 334

Iterations

Iter	Nodes
done	5002
2	3041
1	1144
0	546

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (exp (* 2.0 x)) (sqrt (exp (* 2.0 x)))) (* 1.0 (sqrt 1.0)))
0.0b	(- (+ 1.0 (exp (* 2.0 x))) (* (sqrt 1.0) (sqrt (exp (* 2.0 x)))))
5.8b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.8b	(- (exp x) 1.0)

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-log-exp`
10×	`*-un-lft-identity`
6×	`sqrt-prod`
5×	`difference-of-squares`
4×	`pow1` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sub-neg` `flip3--` `flip--` `distribute-lft-out--`
2×	`sum-log` `pow3`
1×	`+-commutative` `flip3-+` `associate--l+` `sum-cubes` `flip-+`

Counts

4 → 62

Calls

4 calls:

45.0ms	(+ (* (exp (* 2.0 x)) (sqrt (exp (* 2.0 x)))) (* 1.0 (sqrt 1.0)))
81.0ms	(- (+ 1.0 (exp (* 2.0 x))) (* (sqrt 1.0) (sqrt (exp (* 2.0 x)))))
24.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
28.0ms	(- (exp x) 1.0)

series476.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(+ (* (exp (* 2.0 x)) (sqrt (exp (* 2.0 x)))) (* 1.0 (sqrt 1.0)))
142.0ms	(- (+ 1.0 (exp (* 2.0 x))) (* (sqrt 1.0) (sqrt (exp (* 2.0 x)))))
102.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
34.0ms	(- (exp x) 1.0)

simplify7.7s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	4599
2	1286
1	396
0	155

prune944.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ 1.0 (* x 0.5)))
26.1b	(sqrt (+ 2.0 (* x (+ 1.0 (* x 0.5)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 39

Calls

2 calls:

26.0ms	(* x (+ 1.0 (* x 0.5)))
15.0ms	(sqrt (+ 2.0 (* x (+ 1.0 (* x 0.5)))))

series240.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(* x (+ 1.0 (* x 0.5)))
110.0ms	(sqrt (+ 2.0 (* x (+ 1.0 (* x 0.5)))))

simplify2.5s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
2	1138
1	300
0	108

prune400.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

74.2% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.2b

bsearch84.0ms

Steps

Iters	Range		Point
7	-4.6430296561414034e-09	-1.8758842618254644e-11	-4.527236342338421e-09

simplify9.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.0s	6791×	body	10240	exit
1.1s	7438×	body	80	valid
1.1s	12669×	body	80	nan
226.0ms	684×	body	160	valid