Details

analyze913.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample64.0ms

Algorithm

intervals

Results

13.0ms	181×	body	80	valid
9.0ms	20×	body	1280	valid
7.0ms	25×	body	640	valid
7.0ms	25×	body	640	nan
5.0ms	16×	body	1280	nan
4.0ms	20×	body	320	valid
3.0ms	39×	body	80	nan
1.0ms	10×	body	160	valid
1.0ms	5×	body	320	nan
1.0ms	7×	body	160	nan

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	1127	27
1	1127	27

prune12.0ms

Filtered

1 candidates to 1 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: 39.9b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
12.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

15.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
12.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
57.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
186.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify54.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4984	2021
1	4984	2021

prune211.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 2.5b

Counts

93 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
1.0b	(+ (* t t) (/ l (/ x l)))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.5b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
10.0ms	(+ (* t t) (/ l (/ x l)))
9.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
11.0ms	(+ (* t t) (/ l (/ x l)))
14.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
24.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5731	1357

prune176.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	72	10	82

Merged error: 2.4b

Counts

82 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
1.0b	(+ (* t t) (/ l (/ x l)))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.5b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

12.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
10.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
9.0ms	(+ (* t t) (/ l (/ x l)))
15.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
24.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4982	1357
1	4982	1357

prune217.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 2.4b

Counts

87 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
1.0b	(+ (* t t) (/ l (/ x l)))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.5b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

9.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
12.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
9.0ms	(+ (* t t) (/ l (/ x l)))
14.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5527	1378

prune160.0ms

Filtered

61 candidates to 79 candidates (-29.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	76	13	89

Merged error: 2.4b

Counts

89 → 13

regimes670.0ms

Accuracy

74.6% (5.9b remaining)

Error of 9.8b against oracle of 3.9b and baseline of 27.2b

bsearch2.5s

Steps

Iters	Range		Point
9	8.050440477146494e+33	1.0836933855343067e+43	1.5420897965086547e+40
11	-3.3654941915803285e-302	5.524532421258247e-287	-3.3122382461118694e-302
11	-4.320784009633445e-151	-1.9480512183148317e-170	-6.734784418776994e-167
9	-2.2210166600602705e+104	-8.191854810004828e+96	-1.9106906643099877e+104

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	173
1	72	173

end0.0ms

analyze773.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample2.0s

Algorithm

intervals

Results

379.0ms	5125×	body	80	valid
277.0ms	1004×	body	640	valid
276.0ms	788×	body	1280	valid
206.0ms	609×	body	1280	nan
171.0ms	618×	body	640	nan
149.0ms	718×	body	320	valid
104.0ms	1461×	body	80	nan
69.0ms	334×	body	320	nan
51.0ms	365×	body	160	valid
27.0ms	200×	body	160	nan

Details

analyze913.0ms

sample64.0ms

simplify24.0ms

prune12.0ms

localize19.0ms

rewrite46.0ms

series337.0ms

simplify54.0ms

prune211.0ms

localize19.0ms

rewrite34.0ms

series54.0ms

simplify41.0ms

prune176.0ms

localize20.0ms

rewrite43.0ms

series52.0ms

simplify41.0ms

prune217.0ms

localize19.0ms

rewrite41.0ms

series52.0ms

simplify39.0ms

prune160.0ms

regimes670.0ms

bsearch2.5s

simplify2.0ms

end0.0ms

analyze773.0ms

sample2.0s

Profiling