Details

sample306.0ms

Algorithm

intervals

Results

90.0ms	427×	body	80	nan
90.0ms	195×	body	10240	exit
18.0ms	237×	body	80	valid
4.0ms	21×	body	160	valid

simplify3.9s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

47.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
9.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series156.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
48.0ms	(- (exp (* 2.0 x)) 1.0)
39.0ms	(- (exp x) 1.0)

simplify2.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	2920
2	822
1	310
0	130

prune511.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.2b	(- (exp x) 1.0)
4.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`sqrt-prod` `add-log-exp`
5×	`pow1` `add-cube-cbrt` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log`
3×	`sqrt-pow1` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `sum-log` `flip3-+` `exp-to-pow` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
11.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
8.0ms	(- (exp x) 1.0)
14.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series205.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (exp (* 2.0 x)))
64.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)
98.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	3088
3	1194
2	526
1	216
0	102

prune387.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
0.1b	(* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
4.2b	(- (exp x) 1.0)
4.2b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite453.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-prod`
44×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
19×	`pow1`
12×	`sqrt-div` `swap-sqr` `add-cube-cbrt` `distribute-lft-out`
10×	`add-log-exp`
8×	`sqrt-pow1` `pow1/2` `associate-r` `associate-l`
7×	`flip3-+` `flip-+`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up` `difference-of-squares`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `associate-l/` `associate-r/` `flip--`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

11.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
414.0ms	(* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
11.0ms	(- (exp x) 1.0)
14.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series219.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))
79.0ms	(* (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (sqrt (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0))))
25.0ms	(- (exp x) 1.0)
66.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify2.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
3	1896
2	727
1	322
0	150

prune557.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* x 0.5)))
26.2b	(sqrt (+ 2.0 (* x (+ 1.0 (* x 0.5)))))

rewrite17.0ms

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-+` `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 → 37

Calls

2 calls:

12.0ms	(* x (+ 1.0 (* x 0.5)))
4.0ms	(sqrt (+ 2.0 (* x (+ 1.0 (* x 0.5)))))

series183.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* x (+ 1.0 (* x 0.5)))
96.0ms	(sqrt (+ 2.0 (* x (+ 1.0 (* x 0.5)))))

simplify1.4s

Counts

43 → 43

Iterations

Iter	Nodes
done	5005
2	1133
1	297
0	106

prune185.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

78.5% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.4b

bsearch93.0ms

Steps

Iters	Range		Point
7	-0.00027856517442265854	-4.347642122658769e-06	-9.471958066473225e-06

simplify10.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample6.9s

Algorithm

intervals

Results

4.4s	6556×	body	10240	exit
1.4s	12569×	body	80	nan
507.0ms	7407×	body	80	valid
102.0ms	716×	body	160	valid