Details

sample61.0ms

Algorithm

intervals

Results

33.0ms	83×	body	10240	exit
10.0ms	262×	body	80	valid
4.0ms	7×	body	1280	valid
2.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	5

prune2.0ms

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: 0.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.7b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-div` `associate--l+`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(+ 1.0 (exp x))
4.0ms	(log (+ 1.0 (exp x)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(- (log (+ 1.0 (exp x))) (* x y))
7.0ms	(+ 1.0 (exp x))
64.0ms	(log (+ 1.0 (exp x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune102.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Merged error: 0.4b

Counts

55 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(cbrt (+ 1.0 (exp x)))
0.9b	(cbrt (+ 1.0 (exp x)))
0.9b	(cbrt (+ 1.0 (exp x)))
1.4b	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`*-un-lft-identity`
12×	`pow1` `cbrt-prod`
9×	`flip3-+` `pow1/3` `log-pow` `flip-+`
8×	`log-div`
7×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
3×	`distribute-lft-out`
2×	`associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `log-prod` `pow-plus` `prod-exp`

Counts

4 → 69

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (exp x)))
3.0ms	(cbrt (+ 1.0 (exp x)))
3.0ms	(cbrt (+ 1.0 (exp x)))
9.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (+ 1.0 (exp x)))
109.0ms	(cbrt (+ 1.0 (exp x)))
113.0ms	(cbrt (+ 1.0 (exp x)))
177.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	212	675
1	498	601
2	1640	579
3	5001	578

prune213.0ms

Filtered

81 candidates to 64 candidates (79.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Merged error: 0.4b

Counts

84 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.0b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

5.0ms	(* 1/2 (pow x 2))
6.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
8.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 1/2 (pow x 2))
16.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
72.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
51.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune157.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	83	3	86

Merged error: 0.4b

Counts

86 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))
0.0b	(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
0.0b	(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
0.0b	(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
17×	`add-log-exp`
10×	`*-un-lft-identity`
9×	`add-exp-log` `associate-r`
8×	`add-cube-cbrt` `associate-l`
7×	`sum-log`
6×	`add-cbrt-cube`
5×	`sub-neg` `unpow-prod-down` `difference-of-squares`
4×	`pow1` `distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in` `times-frac` `unswap-sqr`
3×	`log-prod` `diff-log` `prod-exp` `unpow2` `sqr-pow`
2×	`+-commutative` `flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+`
1×	`pow-to-exp` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 85

Calls

4 calls:

19.0ms	(* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))
8.0ms	(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
5.0ms	(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
4.0ms	(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))
71.0ms	(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
57.0ms	(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
353.0ms	(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	442	901
1	1771	849
2	5001	840

prune216.0ms

Filtered

97 candidates to 68 candidates (70.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	96	4	100

Merged error: 0.4b

Counts

100 → 4

regimes46.0ms

Accuracy

80.6% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 1.9b

bsearch53.0ms

Steps

Iters	Range		Point
6	-7888799.454350161	-902290.5721441875	-915233.3327664499

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	37
1	41	37

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	2466×	body	10240	exit
337.0ms	8397×	body	80	valid
71.0ms	140×	body	1280	valid
71.0ms	261×	body	640	valid
27.0ms	167×	body	320	valid
12.0ms	117×	body	160	valid

Details

sample61.0ms

simplify6.0ms

prune2.0ms

localize7.0ms

rewrite13.0ms

series126.0ms

simplify47.0ms

prune102.0ms

localize12.0ms

rewrite20.0ms

series512.0ms

simplify55.0ms

prune213.0ms

localize10.0ms

rewrite28.0ms

series166.0ms

simplify45.0ms

prune157.0ms

localize18.0ms

rewrite40.0ms

series557.0ms

simplify57.0ms

prune216.0ms

regimes46.0ms

bsearch53.0ms

simplify1.0ms

end0.0ms

sample1.8s

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