Details

sample396.0ms

Algorithm

intervals

Results

126.0ms	204×	body	10240	exit
113.0ms	238×	body	80	valid
25.0ms	364×	body	80	nan
3.0ms	22×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	181	12
6	489	12
7	1695	12
done	5000	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize24.0ms

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)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
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 → 155

Calls

4 calls:

30.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp x) 1.0)

series290.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
78.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify2.8s

Counts

167 → 167

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1071	2471
3	3554	2362
done	5000	2356

prune584.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
13×	`prod-diff`
10×	`add-log-exp`
7×	`pow1` `fma-neg`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `exp-sum` `flip-+` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*r/` `flip--`
1×	`+-commutative` `pow1/2` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

65.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
19.0ms	(+ (exp x) 1.0)
30.0ms	(- (exp (* 2.0 x)) 1.0)
80.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series277.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
14.0ms	(+ (exp x) 1.0)
45.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify3.7s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	183	1444
1	423	1302
2	1177	1154
3	4997	947
done	5000	947

prune485.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`prod-diff`
8×	`sqrt-pow1` `add-log-exp`
7×	`fma-neg`
6×	`pow1` `exp-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-sum` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `pow1/2` `diff-log` `flip--`
1×	`distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (exp x))
3.0ms	(sqrt (exp x))
17.0ms	(- (exp (* 2.0 x)) 1.0)
76.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series83.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (exp x))
15.0ms	(sqrt (exp x))
28.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.4s

Counts

100 → 100

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	141	1009
1	288	881
2	647	762
3	2356	669
done	5000	651

prune512.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ x (sqrt 2.0)) 0.5 (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))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
176×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
149×	`add-cube-cbrt`
78×	`prod-diff`
67×	`sqrt-prod`
52×	`associate-l`
41×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv`
2×	`frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef` `distribute-lft-out--`

Counts

4 → 300

Calls

4 calls:

1.0ms	(fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0))
137.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
10.0ms	(/ (pow x 2) (sqrt 2.0))
6.0ms	(/ x (sqrt 2.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(fma (/ x (sqrt 2.0)) 0.5 (sqrt 2.0))
105.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
103.0ms	(/ (pow x 2) (sqrt 2.0))
82.0ms	(/ x (sqrt 2.0))

simplify2.9s

Counts

312 → 312

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	480	7223
1	1121	6586
2	3166	5333
done	5000	4815

prune823.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

76.4% (0.6b remaining)

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

bsearch105.0ms

Steps

Iters	Range		Point
8	-8.074815721195404e-17	-5.960240395557237e-20	-5.5218505216622935e-17

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	36	50
done	36	50

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.4s	6749×	body	10240	exit
1.4s	12721×	body	80	nan
559.0ms	7390×	body	80	valid
105.0ms	746×	body	160	valid