Details

analyze769.0ms

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

sample65.0ms

Algorithm

intervals

Results

12.0ms	36×	body	1280	valid
11.0ms	157×	body	80	valid
8.0ms	30×	body	640	valid
6.0ms	18×	body	1280	nan
5.0ms	26×	body	320	valid
5.0ms	19×	body	640	nan
3.0ms	43×	body	80	nan
1.0ms	7×	body	160	valid
1.0ms	4×	body	320	nan
0.0ms	3×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5225	27

prune14.0ms

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: 42.2b

Counts

2 → 2

localize16.0ms

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)
14.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite49.0ms

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)
13.0ms	(- (* (/ (+ 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)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (* (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)
55.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
187.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5044	2021

prune213.0ms

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: 5.0b

Counts

93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
0.6b	(+ (* t t) (/ l (/ x l)))
3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.2b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite36.0ms

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)))
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))))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* t t) (/ l (/ x l)))
16.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify25.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5246	1361

prune167.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 4.9b

Counts

83 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
0.6b	(+ (* t t) (* l (/ l x)))
3.8b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
26.2b	(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))))))

series51.0ms

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

simplify38.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5002	1369

prune146.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	77	11	88

Merged error: 4.9b

Counts

88 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
0.6b	(+ (* t t) (/ l (/ x l)))
3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.2b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite42.0ms

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)))))
11.0ms	(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)))
15.0ms	(+ (* 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))))))

simplify27.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5001	1386

prune153.0ms

Filtered

61 candidates to 79 candidates (-29.5%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	76	14	90

Merged error: 4.9b

Counts

90 → 14

regimes718.0ms

Accuracy

77.3% (5.3b remaining)

Error of 9.3b against oracle of 4.1b and baseline of 27.3b

bsearch331.0ms

Steps

Iters	Range		Point
5	6.062220173833121e+108	1.6886636574577298e+109	1.6665443347108446e+109
9	-1.7292156520845047e-218	-2.513317202480906e-223	-1.711430193012836e-218
10	-4.0752743616416527e-168	-4.435103228596243e-183	-4.526564912154876e-183
6	-6.746387333762877e+151	-6.97085686441427e+150	-2.3599252790391884e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	138	174
1	138	174

end0.0ms

sample1.9s

Algorithm

intervals

Results

378.0ms	5091×	body	80	valid
289.0ms	851×	body	1280	valid
277.0ms	1038×	body	640	valid
194.0ms	590×	body	1280	nan
162.0ms	610×	body	640	nan
139.0ms	657×	body	320	valid
96.0ms	1412×	body	80	nan
67.0ms	338×	body	320	nan
49.0ms	363×	body	160	valid
20.0ms	150×	body	160	nan

Details

analyze769.0ms

sample65.0ms

simplify34.0ms

prune14.0ms

localize16.0ms

rewrite49.0ms

series338.0ms

simplify43.0ms

prune213.0ms

localize16.0ms

rewrite36.0ms

series55.0ms

simplify25.0ms

prune167.0ms

localize19.0ms

rewrite27.0ms

series51.0ms

simplify38.0ms

prune146.0ms

localize18.0ms

rewrite42.0ms

series52.0ms

simplify27.0ms

prune153.0ms

regimes718.0ms

bsearch331.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling