Details

sample405.0ms

Algorithm

intervals

Results

119.0ms	204×	body	10240	exit
61.0ms	22×	body	160	valid
51.0ms	238×	body	80	valid
32.0ms	364×	body	80	nan

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	175	12
6	479	12
7	1665	12
done	5000	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

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))
4.4b	(- (exp (* 2.0 x)) 1.0)
4.5b	(- (exp x) 1.0)

rewrite138.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

30.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
18.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

series324.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
107.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
41.0ms	(- (exp (* 2.0 x)) 1.0)
39.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

135 → 135

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	904	2169
3	2293	2156
done	5001	2154

prune469.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.4b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt`
5×	`sqrt-div`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*r/` `flip--`
1×	`+-commutative` `pow1/2` `exp-sum` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

70.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
17.0ms	(+ (exp x) 1.0)
12.0ms	(- (exp (* 2.0 x)) 1.0)
75.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series238.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
32.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.4s

Counts

68 → 68

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	144	989
1	337	935
2	975	860
3	3361	775
done	5001	757

prune312.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
4.4b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp (+ x x)) (* 1.0 1.0))
4.5b	(- 1.0 (exp x))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `pow-pow` `difference-of-squares`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3--` `diff-log` `cube-prod` `flip--`
2×	`distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `unpow3` `exp-sum` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

10.0ms	(pow (exp x) 3)
24.0ms	(- (exp (* 2.0 x)) 1.0)
61.0ms	(- (exp (+ x x)) (* 1.0 1.0))
12.0ms	(- 1.0 (exp x))

series112.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (exp x) 3)
37.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp (+ x x)) (* 1.0 1.0))
24.0ms	(- 1.0 (exp x))

simplify4.5s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	142	727
1	305	659
2	903	597
3	4842	586
done	5000	586

prune515.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
0.1b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 217

Calls

4 calls:

10.0ms	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
90.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
11.0ms	(/ (pow x 2) (sqrt 2.0))
7.0ms	(/ x (sqrt 2.0))

series439.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(+ (sqrt 2.0) (* 0.5 (/ x (sqrt 2.0))))
100.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
95.0ms	(/ (pow x 2) (sqrt 2.0))
75.0ms	(/ x (sqrt 2.0))

simplify1.7s

Counts

229 → 229

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	270	3092
1	615	2863
2	1914	2584
done	5000	2578

prune700.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

75.9% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.8b

bsearch67.0ms

Steps

Iters	Range		Point
9	-0.00046903783504091863	-4.353488769003373e-11	-2.367867422063156e-05

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	47
1	39	47
done	39	47

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.4s	6749×	body	10240	exit
917.0ms	12721×	body	80	nan
520.0ms	7390×	body	80	valid
119.0ms	746×	body	160	valid