Details

sample356.0ms

Algorithm

intervals

Results

59.0ms	240×	body	10240	exit
14.0ms	421×	body	80	nan
8.0ms	237×	body	80	valid
2.0ms	25×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2657	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 4.9b

Counts

2 → 1

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))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.3b	(- (exp x) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

6×	`flip3--` `flip--`
5×	`sqrt-div`
4×	`associate-/r/` `associate-/l/`
3×	`sqrt-prod`
2×	`sub-neg` `frac-2neg` `clear-num` `div-inv`
1×	`pow1/2` `div-sub`

Counts

4 → 25

Calls

4 calls:

5.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
6.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp x) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
65.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	214	267
1	556	263
2	1769	256
3	5002	254

prune108.0ms

Filtered

37 candidates to 27 candidates (73.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	3	38

Merged error: 0.0b

Counts

38 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/r/`
3×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`
2×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l/`
1×	`sub-neg` `div-sub` `fma-udef`

Counts

4 → 22

Calls

4 calls:

7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
3.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0ms	(- (exp (* 2.0 x)) 1.0)

series248.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
65.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	209	259
1	627	255
2	2659	230
3	5001	230

prune108.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0.0b

Counts

37 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ 1 (/ (+ (exp x) 1.0) (- (exp (* 2 x)) (* 1.0 1.0)))))
0.0b	(/ (+ (exp x) 1.0) (- (exp (* 2 x)) (* 1.0 1.0)))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.2b	(- (exp (* 2 x)) (* 1.0 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-/r/`
15×	`associate-/r*`
13×	`*-commutative`
9×	`exp-lft-sqr`
6×	`associate-/l/` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-2neg` `clear-num` `div-inv`
2×	`sub-neg` `flip3-+` `prod-diff` `flip-+`
1×	`fma-neg` `div-sub`

Counts

4 → 42

Calls

4 calls:

11.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ 1 (/ (+ (exp x) 1.0) (- (exp (* 2 x)) (* 1.0 1.0)))))
8.0ms	(/ (+ (exp x) 1.0) (- (exp (* 2 x)) (* 1.0 1.0)))
3.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp (* 2 x)) (* 1.0 1.0))

series170.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ 1 (/ (+ (exp x) 1.0) (- (exp (* 2 x)) (* 1.0 1.0)))))
41.0ms	(/ (+ (exp x) 1.0) (- (exp (* 2 x)) (* 1.0 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
18.0ms	(- (exp (* 2 x)) (* 1.0 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	319	377
1	1182	361
2	5001	344

prune155.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	53	4	57

Merged error: 0.0b

Counts

57 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (exp (* 2 x)) (exp (* 2 x)))
0.1b	(pow (exp (* 2 x)) 3)
5.1b	(- (pow (exp (* 2 x)) 3) (pow (* 1.0 1.0) 3))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-commutative`
19×	`unpow-prod-down`
15×	`exp-lft-sqr`
14×	`exp-prod` `sqr-pow`
12×	`prod-diff`
9×	`unpow3`
6×	`difference-of-squares`
3×	`fma-neg`
2×	`sub-neg` `flip3--` `pow-pow` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--`
1×	`difference-cubes` `pow2` `pow-to-exp` `swap-sqr` `associate-r` `associate-l` `pow-exp` `prod-exp` `unswap-sqr`

Counts

4 → 50

Calls

4 calls:

6.0ms	(* (exp (* 2 x)) (exp (* 2 x)))
3.0ms	(pow (exp (* 2 x)) 3)
9.0ms	(- (pow (exp (* 2 x)) 3) (pow (* 1.0 1.0) 3))
4.0ms	(- (exp (* 2.0 x)) 1.0)

series112.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (exp (* 2 x)) (exp (* 2 x)))
26.0ms	(pow (exp (* 2 x)) 3)
44.0ms	(- (pow (exp (* 2 x)) 3) (pow (* 1.0 1.0) 3))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify165.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	287	472
1	952	323
2	4487	283
3	5001	281

prune174.0ms

Filtered

62 candidates to 32 candidates (51.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	63	3	66

Merged error: 0b

Counts

66 → 3

regimes27.0ms

Accuracy

77.8% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.9b

bsearch2.0ms

Steps

Iters	Range		Point
0	-1.4365382038701608e-08	-1.394695875033139e-08	-1.41561703945165e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	44
1	52	44

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	6812×	body	10240	exit
395.0ms	12826×	body	80	nan
247.0ms	7417×	body	80	valid
56.0ms	721×	body	160	valid