Details

sample280.0ms

Algorithm

intervals

Results

137.0ms	211×	body	10240	exit
25.0ms	409×	body	80	nan
18.0ms	240×	body	80	valid
3.0ms	18×	body	160	valid

simplify979.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	179	12
6	752	12
done	5000	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize19.0ms

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))
3.9b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite156.0ms

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:

51.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
43.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

series276.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
77.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms	(- (exp (* 2.0 x)) 1.0)
46.0ms	(- (exp x) 1.0)

simplify920.0ms

Counts

135 → 135

Iterations

Useful iterations: done (911.0ms)

Iter	Nodes	Cost
0	189	2376
1	396	2279
2	1220	2169
done	5000	2156

prune446.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(sqrt (+ (exp x) 1.0))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
18.0ms	(sqrt (+ (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
83.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series111.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
39.0ms	(sqrt (+ (exp x) 1.0))
35.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: 3 (974.0ms)

Iter	Nodes	Cost
0	127	697
1	293	657
2	950	598
3	4122	585
done	5001	585

prune302.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.3b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

19.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
21.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
13.0ms	(- (exp (* 2.0 x)) 1.0)
68.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series172.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
30.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
45.0ms	(- (exp (* 2.0 x)) 1.0)
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: 2 (359.0ms)

Iter	Nodes	Cost
0	140	1353
1	385	1148
2	1875	1025
done	5002	1025

prune451.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 0.5 x) 1.0))
29.4b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
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:

35.0ms	(* x (+ (* 0.5 x) 1.0))
5.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series208.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(* x (+ (* 0.5 x) 1.0))
119.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify968.0ms

Counts

43 → 43

Iterations

Useful iterations: 2 (262.0ms)

Iter	Nodes	Cost
0	106	598
1	300	547
2	1430	513
done	5002	513

prune122.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

77.1% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.9b

bsearch49.0ms

Steps

Iters	Range		Point
6	-1.1215045282520511e-10	-1.846828719233542e-11	-1.1094191668549575e-10

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	36
1	32	36
done	32	36

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.6s	6723×	body	10240	exit
1.1s	12665×	body	80	nan
775.0ms	7393×	body	80	valid
117.0ms	732×	body	160	valid