Details

analyze761.0ms

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

sample61.0ms

Algorithm

intervals

Results

12.0ms	168×	body	80	valid
9.0ms	27×	body	640	valid
8.0ms	24×	body	1280	valid
4.0ms	23×	body	320	valid
4.0ms	13×	body	1280	nan
4.0ms	14×	body	640	nan
3.0ms	44×	body	80	nan
2.0ms	14×	body	160	valid
1.0ms	7×	body	320	nan
1.0ms	6×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5225	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: 40.2b

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))))
0.4b	(* (sqrt 2.0) t)
14.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite52.0ms

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

series346.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* (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)
58.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
191.0ms	(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

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: 4.1b

Counts

93 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.2b	(+ (* t t) (/ l (/ x l)))
3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.3b	(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)))
18.0ms	(+ (* 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))))))

simplify25.0ms

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	70	7	77
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 4.1b

Counts

83 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.2b	(+ (* t t) (* l (/ l x)))
3.8b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
26.3b	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite28.0ms

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)))
10.0ms	(+ (* 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))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* t t) (* l (/ l x)))
15.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
25.0ms	(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 (31.0ms)

Iter	Nodes	Cost
0	5002	1369

prune155.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

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: 4.1b

Counts

89 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
1.2b	(+ (* t t) (/ l (/ x l)))
3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.3b	(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:

10.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
11.0ms	(+ (* t t) (/ l (/ x l)))
11.0ms	(+ (* 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)))))
25.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify27.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5257	1357

prune161.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	77	12	89

Merged error: 4.1b

Counts

89 → 12

regimes823.0ms

Accuracy

77.3% (5.5b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 28.0b

bsearch352.0ms

Steps

Iters	Range		Point
8	8.148651374270388e+49	6.2118072606805805e+53	6.924374475501798e+51
7	1.2479894500697624e-167	2.154138551810523e-165	1.2728735809299012e-167
10	2.7869172044264258e-291	3.7092726544946636e-278	3.649256253420378e-278
5	-1.5831300867795434e+132	-6.097952887835775e+131	-9.900843518970186e+131

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	163	148
1	163	148

end0.0ms

sample1.9s

Algorithm

intervals

Results

363.0ms	5186×	body	80	valid
268.0ms	803×	body	1280	valid
253.0ms	962×	body	640	valid
189.0ms	576×	body	1280	nan
160.0ms	636×	body	640	nan
131.0ms	663×	body	320	valid
97.0ms	1452×	body	80	nan
63.0ms	330×	body	320	nan
51.0ms	386×	body	160	valid
23.0ms	166×	body	160	nan

Details

analyze761.0ms

sample61.0ms

simplify34.0ms

prune12.0ms

localize16.0ms

rewrite52.0ms

series346.0ms

simplify43.0ms

prune210.0ms

localize18.0ms

rewrite36.0ms

series55.0ms

simplify25.0ms

prune179.0ms

localize16.0ms

rewrite28.0ms

series52.0ms

simplify38.0ms

prune155.0ms

localize19.0ms

rewrite43.0ms

series52.0ms

simplify27.0ms

prune161.0ms

regimes823.0ms

bsearch352.0ms

simplify3.0ms

end0.0ms

sample1.9s

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