Details

sample248.0ms

Algorithm

intervals

Results

28.0ms	73×	body	1280	valid
10.0ms	43×	body	640	valid
5.0ms	73×	body	80	overflowed
5.0ms	32×	body	320	valid
4.0ms	95×	body	80	valid
1.0ms	14×	body	160	valid

simplify426.0ms

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

prune5.0ms

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: 39.9b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.9b	(- (exp (* 2.0 x)) 1.0)
4.9b	(- (exp x) 1.0)

rewrite34.0ms

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	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
3.0ms	(- (exp (* 2.0 x)) 1.0)
10.0ms	(- (exp x) 1.0)

simplify121.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

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

prune253.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0.0b

Counts

136 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
9.6b	(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:

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

prune66.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Merged error: 0b

Counts

45 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
0.1b	(* (fabs (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
10.5b	(cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
10.5b	(cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

8.0ms	(sqrt (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
10.0ms	(* (fabs (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
5.0ms	(cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
5.0ms	(cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
19.0ms	(* (fabs (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
8.0ms	(cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
10.0ms	(cbrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	545	1415
1	1904	1345
2	5001	1229

prune277.0ms

Filtered

73 candidates to 86 candidates (-17.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* 2.0 x)))
0.2b	(sqrt (exp (* 2.0 x)))
4.9b	(- (exp x) 1.0)
4.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 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)))
4.0ms	(- (exp x) 1.0)
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
3.0ms	(sqrt (exp (* 2.0 x)))
2.0ms	(- (exp x) 1.0)
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify103.0ms

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

prune161.0ms

Filtered

49 candidates to 74 candidates (-51.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	74	3	77

Merged error: 0b

Counts

77 → 3

regimes38.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.7b

bsearch16.0ms

Steps

Iters	Range		Point
8	-3.831560156749637e-05	-7.511273327943636e-10	-1.2483850857532933e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.8s

Algorithm

intervals

Results

830.0ms	2367×	body	1280	valid
368.0ms	1652×	body	640	valid
124.0ms	2839×	body	80	valid
120.0ms	808×	body	320	valid
97.0ms	2516×	body	80	overflowed
40.0ms	391×	body	160	valid

Details

sample248.0ms

simplify426.0ms

prune5.0ms

localize26.0ms

rewrite34.0ms

series32.0ms

simplify121.0ms

prune253.0ms

localize6.0ms

rewrite11.0ms

series11.0ms

simplify38.0ms

prune66.0ms

localize10.0ms

rewrite29.0ms

series46.0ms

simplify55.0ms

prune277.0ms

localize13.0ms

rewrite15.0ms

series13.0ms

simplify103.0ms

prune161.0ms

regimes38.0ms

bsearch16.0ms

simplify2.0ms

end0.0ms

sample1.8s

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