Details

sample245.0ms

Algorithm

intervals

Results

194.0ms	235×	body	80	overflowed
15.0ms	384×	body	80	nan
12.0ms	238×	body	80	valid
2.0ms	24×	body	160	valid

simplify72.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.5b

Counts

2 → 1

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))
5.0b	(- (exp (* 2.0 x)) 1.0)
5.0b	(- (exp x) 1.0)

rewrite33.0ms

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:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series33.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms	(- (exp (* 2.0 x)) 1.0)
11.0ms	(- (exp x) 1.0)

simplify132.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune243.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* 2.0 x)))
0.2b	(sqrt (exp (* 2.0 x)))
5.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.0b	(- (exp x) 1.0)

rewrite15.0ms

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:

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

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
3.0ms	(sqrt (exp (* 2.0 x)))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.0ms	(- (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	5002	361

prune159.0ms

Filtered

49 candidates to 74 candidates (-51.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Merged error: 0b

Counts

78 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (neg (* 1.0 1.0)) (pow (exp 2.0) (* 2 x))) (+ (exp (* 2.0 x)) 1.0)) (- (exp x) 1.0))
0.0b	(pow (exp 2.0) (* 2 x))
4.9b	(+ (neg (* 1.0 1.0)) (pow (exp 2.0) (* 2 x)))
5.0b	(- (exp x) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

229×	`*-un-lft-identity`
206×	`times-frac`
131×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
49×	`distribute-lft-out`
24×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/l*`
14×	`associate-/r/`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+` `div-inv`
5×	`pow1` `associate-/r*`
4×	`pow-pow`
3×	`cbrt-undiv` `unpow-prod-down` `exp-prod` `div-exp`
2×	`neg-sub0` `associate-+l-` `flip3--` `div-sub` `sum-log` `flip--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-unpow` `frac-2neg` `diff-log` `neg-log` `pow-exp` `clear-num` `associate-/l/` `sqr-pow`

Counts

4 → 201

Calls

4 calls:

18.0ms	(/ (/ (+ (neg (* 1.0 1.0)) (pow (exp 2.0) (* 2 x))) (+ (exp (* 2.0 x)) 1.0)) (- (exp x) 1.0))
3.0ms	(pow (exp 2.0) (* 2 x))
6.0ms	(+ (neg (* 1.0 1.0)) (pow (exp 2.0) (* 2 x)))
4.0ms	(- (exp x) 1.0)

series32.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (/ (+ (neg (* 1.0 1.0)) (pow (exp 2.0) (* 2 x))) (+ (exp (* 2.0 x)) 1.0)) (- (exp x) 1.0))
3.0ms	(pow (exp 2.0) (* 2 x))
6.0ms	(+ (neg (* 1.0 1.0)) (pow (exp 2.0) (* 2 x)))
2.0ms	(- (exp x) 1.0)

simplify94.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	789	4022
1	3207	3906
2	5001	3885

prune541.0ms

Filtered

131 candidates to 213 candidates (-62.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	213	4	217

Merged error: 0b

Counts

217 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
27.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite11.0ms

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:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series11.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* x (+ 1.0 (* 0.5 x)))
6.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	279	280
1	1132	268
2	5002	256

prune54.0ms

Filtered

30 candidates to 43 candidates (-43.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	43	4	47

Merged error: 0b

Counts

47 → 4

regimes42.0ms

Accuracy

78.3% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.5b

bsearch19.0ms

Steps

Iters	Range		Point
9	-5.638243373460967	-1.2795655736726249e-08	-0.00018690287297781785

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	26
1	45	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

505.0ms	12702×	body	80	nan
322.0ms	7411×	body	80	valid
255.0ms	6726×	body	80	overflowed
75.0ms	717×	body	160	valid

Details

sample245.0ms

simplify72.0ms

prune4.0ms

localize11.0ms

rewrite33.0ms

series33.0ms

simplify132.0ms

prune243.0ms

localize13.0ms

rewrite15.0ms

series15.0ms

simplify102.0ms

prune159.0ms

localize20.0ms

rewrite42.0ms

series32.0ms

simplify94.0ms

prune541.0ms

localize6.0ms

rewrite11.0ms

series11.0ms

simplify38.0ms

prune54.0ms

regimes42.0ms

bsearch19.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling