Details

sample311.0ms

Algorithm

intervals

Results

17.0ms	344×	body	80	nan
11.0ms	234×	body	80	valid
10.0ms	222×	body	80	overflowed
3.0ms	24×	body	160	valid

simplify74.0ms

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

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: 4.8b

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))
5.3b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite48.0ms

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:

23.0ms	(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)

series206.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify125.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (111.0ms)

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

prune313.0ms

Filtered

135 candidates to 92 candidates (68.1%)

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: 0.0b

Counts

136 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.4b	(- (exp x) 1.0)

rewrite16.0ms

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)

series110.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
22.0ms	(sqrt (exp (* 2.0 x)))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5002	361

prune183.0ms

Filtered

74 candidates to 49 candidates (66.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Merged error: 0.0b

Counts

78 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
0.1b	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.4b	(- (exp x) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`sqrt-prod`
24×	`cbrt-prod`
21×	`difference-of-squares`
18×	`unpow-prod-down` `cube-prod`
11×	`distribute-lft-out--`
10×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

8.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
8.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3)
52.0ms	(cbrt (pow (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) 3))
47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
18.0ms	(- (exp x) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	357	1065
1	1371	995
2	5001	983

prune233.0ms

Filtered

116 candidates to 55 candidates (47.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	116	3	119

Merged error: 0.0b

Counts

119 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
0.0b	(* x (+ 1.0 (* 0.5 x)))
23.8b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `sqrt-prod` `flip-+`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

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

series169.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (* x (+ 1.0 (* 0.5 x))) 2.0)
68.0ms	(* x (+ 1.0 (* 0.5 x)))
80.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	308	385
1	1305	364
2	5001	352

prune97.0ms

Filtered

59 candidates to 43 candidates (72.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	59	3	62

Merged error: 0.0b

Counts

62 → 3

regimes26.0ms

Accuracy

79.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.3b

bsearch38.0ms

Steps

Iters	Range		Point
7	-0.0007090918830877794	-3.895343399462064e-06	-1.1898853542802406e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

528.0ms	12637×	body	80	nan
344.0ms	7461×	body	80	valid
267.0ms	6559×	body	80	overflowed
71.0ms	681×	body	160	valid

Details

sample311.0ms

simplify74.0ms

prune4.0ms

localize12.0ms

rewrite48.0ms

series206.0ms

simplify125.0ms

prune313.0ms

localize15.0ms

rewrite16.0ms

series110.0ms

simplify107.0ms

prune183.0ms

localize18.0ms

rewrite30.0ms

series241.0ms

simplify48.0ms

prune233.0ms

localize7.0ms

rewrite17.0ms

series169.0ms

simplify44.0ms

prune97.0ms

regimes26.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample1.5s

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