Details

sample199.0ms

Algorithm

intervals

Results

59.0ms	405×	body	80	nan
55.0ms	192×	body	10240	exit
12.0ms	235×	body	80	valid
3.0ms	24×	body	160	valid

simplify987.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize41.0ms

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))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp x) 1.0)

rewrite167.0ms

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:

33.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
77.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

series317.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
50.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(- (exp x) 1.0)

simplify841.0ms

Counts

135 → 135

Iterations

Useful iterations: done (826.0ms)

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

prune618.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite213.0ms

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:

20.0ms	(+ (exp x) 1.0)
82.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
13.0ms	(- (exp (* 2.0 x)) 1.0)
95.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series230.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (exp x) 1.0)
163.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
30.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify750.0ms

Counts

68 → 68

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	144	989
1	351	935
2	1187	860
done	5001	777

prune458.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
0.1b	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp (* 2 x)) 1.0)

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`flip3--` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-r` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`sub-neg` `associate-r/` `associate-l` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

93.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
116.0ms	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (* 2 x)) 1.0)

series301.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
93.0ms	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
38.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (* 2 x)) 1.0)

simplify1.9s

Counts

108 → 108

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	169	1914
1	482	1851
2	2377	1651
done	5000	1643

prune557.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
0.1b	(pow (- (exp (* 2.0 x)) 1.0) 3)
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite169.0ms

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:

29.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
36.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
26.0ms	(- (exp (* 2.0 x)) 1.0)
75.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series150.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
62.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
36.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	140	1353
1	385	1148
2	1872	1025
done	5001	1025

prune536.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes46.0ms

Accuracy

76.2% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.7b

bsearch79.0ms

Steps

Iters	Range		Point
8	-3.092080667674878e-11	-1.991891315317258e-14	-3.031481252135206e-11

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	32	33
done	32	33

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.9s	6601×	body	10240	exit
1.5s	12770×	body	80	nan
563.0ms	7395×	body	80	valid
102.0ms	718×	body	160	valid