Details

analyze933.0ms

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

sample71.0ms

Algorithm

intervals

Results

14.0ms	54×	body	640	valid
10.0ms	143×	body	80	valid
10.0ms	29×	body	1280	valid
8.0ms	14×	body	1280	nan
7.0ms	25×	body	640	nan
4.0ms	22×	body	320	valid
3.0ms	44×	body	80	nan
1.0ms	6×	body	320	nan
1.0ms	8×	body	160	valid
0.0ms	3×	body	160	nan

simplify33.0ms

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: 48.1b

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)
14.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.2b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite54.0ms

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:

18.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
15.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
14.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series345.0ms

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))
190.0ms	(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

prune194.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Merged error: 3.5b

Counts

93 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.0b	(+ (* t t) (/ l (/ x l)))
3.2b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.4b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite40.0ms

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)
13.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
10.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify25.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5246	1361

prune162.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	72	8	80

Merged error: 3.4b

Counts

80 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
1.0b	(+ (* t t) (/ l (/ x l)))
3.2b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.4b	(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)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
10.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series54.0ms

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)))
17.0ms	(+ (* 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))))))

simplify25.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5257	1357

prune209.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 3.4b

Counts

85 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.0b	(+ (* t t) (* l (/ l x)))
3.2b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
27.4b	(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)))
9.0ms	(+ (* 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))))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
10.0ms	(+ (* t t) (* l (/ l x)))
14.0ms	(+ (* 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))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5002	1369

prune111.0ms

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: 3.4b

Counts

88 → 11

regimes325.0ms

Accuracy

78.5% (5.0b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 27.4b

bsearch298.0ms

Steps

Iters	Range		Point
8	5.078752419234412e+125	4.1380793694440134e+128	3.988258365544033e+126
8	-2.5949801378023832e-257	-1.0707401225500955e-261	-2.547810898389432e-257
7	-1.407075432503316e-164	-2.6527296033754943e-166	-2.6827523042144143e-166
7	-2.1479671810792464e+154	-1.0691138239515233e+153	-5.786161624159091e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	150	188
1	150	188

end0.0ms

sample1.9s

Algorithm

intervals

Results

367.0ms	5138×	body	80	valid
301.0ms	859×	body	1280	valid
265.0ms	982×	body	640	valid
192.0ms	582×	body	1280	nan
168.0ms	636×	body	640	nan
128.0ms	626×	body	320	valid
101.0ms	1493×	body	80	nan
64.0ms	313×	body	320	nan
54.0ms	395×	body	160	valid
23.0ms	174×	body	160	nan

Details

analyze933.0ms

sample71.0ms

simplify33.0ms

prune12.0ms

localize16.0ms

rewrite54.0ms

series345.0ms

simplify43.0ms

prune194.0ms

localize17.0ms

rewrite40.0ms

series52.0ms

simplify25.0ms

prune162.0ms

localize22.0ms

rewrite43.0ms

series54.0ms

simplify25.0ms

prune209.0ms

localize16.0ms

rewrite27.0ms

series53.0ms

simplify39.0ms

prune111.0ms

regimes325.0ms

bsearch298.0ms

simplify3.0ms

end0.0ms

sample1.9s

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