Details

analyze774.0ms

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

sample58.0ms

Algorithm

intervals

Results

13.0ms	163×	body	80	valid
8.0ms	31×	body	640	valid
7.0ms	23×	body	1280	valid
4.0ms	17×	body	640	nan
4.0ms	22×	body	320	valid
3.0ms	9×	body	1280	nan
3.0ms	43×	body	80	nan
2.0ms	17×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	4×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5225	27

prune11.0ms

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

localize15.0ms

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))))
0.4b	(* (sqrt 2.0) t)
12.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite51.0ms

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:

17.0ms	(/ (* (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)
15.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (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))
185.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5044	2021

prune210.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 3.6b

Counts

93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
0.6b	(+ (* t t) (/ l (/ x l)))
3.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.2b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite38.0ms

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)
11.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
11.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
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))))))

simplify28.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5246	1361

prune179.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 3.5b

Counts

83 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
0.6b	(+ (* t t) (* l (/ l x)))
3.4b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
25.2b	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-*r/`
8×	`add-cube-cbrt` `*-un-lft-identity` `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)
4.0ms	(+ (* t t) (* l (/ l x)))
8.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* t t) (* l (/ l x)))
14.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
26.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5002	1369

prune150.0ms

Filtered

54 candidates to 77 candidates (-42.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	77	12	89

Merged error: 3.5b

Counts

89 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
0.6b	(+ (* t t) (/ l (/ x l)))
3.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.2b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite40.0ms

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:

8.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (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))))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
9.0ms	(+ (* t t) (/ l (/ x l)))
15.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify25.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5001	1386

prune154.0ms

Filtered

60 candidates to 79 candidates (-31.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	77	14	91

Merged error: 3.5b

Counts

91 → 14

regimes677.0ms

Accuracy

77.3% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.3b

bsearch596.0ms

Steps

Iters	Range		Point
7	1.1598396644452419e+64	2.4294870855720693e+66	1.6275844446328344e+66
8	3.108440259560079e-156	3.3390910847991837e-152	3.1695088296437016e-156
8	2.560457474548375e-231	1.0704869587886642e-228	1.0593625536365536e-228
9	-7.984222049081711e-229	-1.191304036239433e-237	-7.795682222360029e-229
10	-4.704805681313936e-149	-1.752888681083758e-162	-1.7771056583212281e-162
10	-1.6352364842941578e+105	-4.601103848098356e+93	-3.2170273163093555e+100

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	144	199
1	144	199

end0.0ms

sample1.9s

Algorithm

intervals

Results

362.0ms	5117×	body	80	valid
286.0ms	847×	body	1280	valid
273.0ms	1046×	body	640	valid
200.0ms	601×	body	1280	nan
147.0ms	576×	body	640	nan
127.0ms	650×	body	320	valid
93.0ms	1414×	body	80	nan
62.0ms	316×	body	320	nan
47.0ms	340×	body	160	valid
22.0ms	169×	body	160	nan

Details

analyze774.0ms

sample58.0ms

simplify34.0ms

prune11.0ms

localize15.0ms

rewrite51.0ms

series334.0ms

simplify42.0ms

prune210.0ms

localize16.0ms

rewrite38.0ms

series51.0ms

simplify28.0ms

prune179.0ms

localize16.0ms

rewrite27.0ms

series54.0ms

simplify40.0ms

prune150.0ms

localize18.0ms

rewrite40.0ms

series54.0ms

simplify25.0ms

prune154.0ms

regimes677.0ms

bsearch596.0ms

simplify3.0ms

end0.0ms

sample1.9s

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