Details

sample341.0ms

Algorithm

intervals

Results

113.0ms	218×	body	10240	exit
90.0ms	395×	body	80	nan
18.0ms	235×	body	80	valid
4.0ms	23×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize36.0ms

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)
4.4b	(- (exp x) 1.0)

rewrite194.0ms

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:

52.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
84.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

series350.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
98.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
48.0ms	(- (exp (* 2.0 x)) 1.0)
42.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: done (1.1s)

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

prune771.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (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))

rewrite188.0ms

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:

23.0ms	(sqrt (+ (exp x) 1.0))
18.0ms	(+ (exp x) 1.0)
25.0ms	(- (exp (* 2.0 x)) 1.0)
120.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series170.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (exp x) 1.0))
17.0ms	(+ (exp x) 1.0)
45.0ms	(- (exp (* 2.0 x)) 1.0)
41.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify3.0s

Counts

68 → 68

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	127	697
1	292	657
2	936	598
3	4004	585
done	5002	585

prune515.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.1b	(* (sqrt (sqrt (+ (exp x) 1.0))) (sqrt (sqrt (+ (exp x) 1.0))))
4.4b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

22.0ms	(+ (exp x) 1.0)
126.0ms	(* (sqrt (sqrt (+ (exp x) 1.0))) (sqrt (sqrt (+ (exp x) 1.0))))
23.0ms	(- (exp (* 2.0 x)) 1.0)
102.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (exp x) 1.0)
60.0ms	(* (sqrt (sqrt (+ (exp x) 1.0))) (sqrt (sqrt (+ (exp x) 1.0))))
47.0ms	(- (exp (* 2.0 x)) 1.0)
35.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.0s

Counts

140 → 140

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	196	2210
1	433	1393
2	1744	1279
done	5000	1267

prune823.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 0.5 x) 1.0))
27.0b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite71.0ms

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:

58.0ms	(* x (+ (* 0.5 x) 1.0))
11.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series254.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(* x (+ (* 0.5 x) 1.0))
138.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify1.2s

Counts

43 → 43

Iterations

Useful iterations: 2 (352.0ms)

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

prune225.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes71.0ms

Accuracy

76% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.1b

bsearch62.0ms

Steps

Iters	Range		Point
5	-4.5846337071089676e-10	-2.188605173615867e-10	-4.5450129290399687e-10

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample9.9s

Algorithm

intervals

Results

5.7s	6881×	body	10240	exit
1.6s	7412×	body	80	valid
1.3s	12981×	body	80	nan
233.0ms	717×	body	160	valid