Details

sample317.0ms

Algorithm

intervals

Results

23.0ms	450×	body	80	nan
15.0ms	239×	body	80	valid
12.0ms	252×	body	80	overflowed
3.0ms	22×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 4.2b

localize11.0ms

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)
4.7b	(- (exp x) 1.0)

rewrite53.0ms

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:

13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
24.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series196.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

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

prune336.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* 2.0 x)))
0.2b	(sqrt (exp (* 2.0 x)))
4.7b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-pow1`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

1.0ms	(sqrt (exp (* 2.0 x)))
1.0ms	(sqrt (exp (* 2.0 x)))
9.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series106.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (exp (* 2.0 x)))
25.0ms	(sqrt (exp (* 2.0 x)))
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5001	361

prune211.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (* 1/2 x))
0.2b	(sqrt (exp (* 2.0 x)))
4.7b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
6×	`pow1` `sqrt-prod`
5×	`unpow-prod-down`
4×	`add-exp-log` `exp-prod` `pow-pow` `add-cbrt-cube`
3×	`sqrt-pow1` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `exp-to-pow` `pow1/2` `pow-exp`

Counts

4 → 66

Calls

4 calls:

2.0ms	(pow (exp 2.0) (* 1/2 x))
1.0ms	(sqrt (exp (* 2.0 x)))
12.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series123.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (exp 2.0) (* 1/2 x))
21.0ms	(sqrt (exp (* 2.0 x)))
55.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	243	428
1	686	409
2	2418	406
3	5002	404

prune273.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (* 1/2 x))
0.2b	(sqrt (exp (* 2.0 x)))
4.7b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
6×	`pow1` `sqrt-prod`
5×	`unpow-prod-down`
4×	`add-exp-log` `exp-prod` `pow-pow` `add-cbrt-cube`
3×	`sqrt-pow1` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `exp-to-pow` `pow1/2` `pow-exp`

Counts

4 → 66

Calls

4 calls:

2.0ms	(pow (exp 2.0) (* 1/2 x))
1.0ms	(sqrt (exp (* 2.0 x)))
12.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series123.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (exp 2.0) (* 1/2 x))
21.0ms	(sqrt (exp (* 2.0 x)))
55.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	243	428
1	686	409
2	2418	406
3	5002	404

prune298.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes26.0ms

Accuracy

86.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 3.2b

bsearch36.0ms

Steps

Iters	Range		Point
5	-4.613206121218691e-07	-2.182603019671814e-07	-4.407566599899106e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	22
1	36	22

end0.0ms

sample1.8s

Algorithm

intervals

Results

668.0ms	12961×	body	80	nan
408.0ms	7437×	body	80	valid
342.0ms	6918×	body	80	overflowed
87.0ms	700×	body	160	valid