Details

sample339.0ms

Algorithm

intervals

Results

52.0ms	228×	body	10240	exit
12.0ms	397×	body	80	nan
8.0ms	235×	body	80	valid
2.0ms	24×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize12.0ms

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))
4.2b	(- (exp (* 2.0 x)) 1.0)
4.3b	(- (exp x) 1.0)

rewrite46.0ms

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:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
32.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify123.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune361.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
4.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.3b	(- (exp x) 1.0)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`sqrt-prod`
9×	`associate-r` `add-log-exp` `difference-of-squares`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3--` `associate-l` `flip--` `distribute-lft-out--`
4×	`frac-times` `sub-neg`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-r/` `associate-l/` `distribute-lft-out`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

1.0ms	(sqrt (exp (* 2.0 x)))
50.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
113.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	322	888
1	1345	780
2	5001	754

prune291.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (pow (exp 2.0) (/ x 2)) (sqrt 1.0)))
4.3b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
4.3b	(- (exp x) 1.0)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`difference-of-squares`
11×	`sqrt-prod`
10×	`associate-r`
9×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3--` `associate-l` `flip--`
4×	`frac-times` `sub-neg` `unpow-prod-down` `sqr-pow`
3×	`sqrt-pow1` `flip3-+` `flip-+` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-r/` `associate-l/` `distribute-lft-out`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

1.0ms	(sqrt (exp (* 2.0 x)))
55.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (pow (exp 2.0) (/ x 2)) (sqrt 1.0)))
15.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series220.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
127.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (pow (exp 2.0) (/ x 2)) (sqrt 1.0)))
53.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	384	979
1	1544	911
2	5001	906

prune371.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (sqrt (exp (* 2.0 x))))
0.1b	(* (cbrt (sqrt (exp (* 2.0 x)))) (cbrt (sqrt (exp (* 2.0 x)))))
4.3b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
4.3b	(- (exp x) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
46×	`cbrt-prod`
26×	`sqrt-prod`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
11×	`pow1` `swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`add-log-exp`
7×	`pow1/3` `difference-of-squares`
6×	`add-exp-log`
4×	`add-cbrt-cube`
2×	`sub-neg` `unpow-prod-down` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--` `sqr-pow`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

4.0ms	(cbrt (sqrt (exp (* 2.0 x))))
11.0ms	(* (cbrt (sqrt (exp (* 2.0 x)))) (cbrt (sqrt (exp (* 2.0 x)))))
12.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series283.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (sqrt (exp (* 2.0 x))))
111.0ms	(* (cbrt (sqrt (exp (* 2.0 x)))) (cbrt (sqrt (exp (* 2.0 x)))))
52.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	299	1098
1	871	1031
2	3219	961
3	5003	932

prune427.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

73% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.8b

bsearch55.0ms

Steps

Iters	Range		Point
8	-9.296451012434831e-16	-3.148161800826367e-19	-6.977161741978232e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6819×	body	10240	exit
386.0ms	12561×	body	80	nan
255.0ms	7396×	body	80	valid
56.0ms	727×	body	160	valid