Details

sample108.0ms

Algorithm

intervals

Results

24.0ms	359×	body	80	nan
11.0ms	159×	body	80	valid
10.0ms	30×	body	1280	valid
9.0ms	37×	body	640	valid
8.0ms	31×	body	640	nan
6.0ms	20×	body	1280	nan
4.0ms	21×	body	320	valid
2.0ms	11×	body	320	nan
1.0ms	9×	body	160	valid
1.0ms	5×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

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: 43.9b

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)
12.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.0b	(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 → 80

Calls

4 calls:

18.0ms	(/ (* (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)
14.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
16.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series345.0ms

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)
58.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
192.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5044	2025

prune198.0ms

Filtered

67 candidates to 92 candidates (-37.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 4.9b

Counts

94 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* t t) (/ l (/ x l)))
0.5b	(* (sqrt 2.0) t)
3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
28.1b	(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:

12.0ms	(+ (* t t) (/ l (/ x l)))
5.0ms	(* (sqrt 2.0) t)
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
12.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify28.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5246	1361

prune150.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 4.9b

Counts

80 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
0.4b	(+ (* t t) (/ l (/ x l)))
3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
28.1b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite45.0ms

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:

11.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
12.0ms	(+ (* 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))))))

series55.0ms

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

simplify26.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5257	1357

prune188.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Merged error: 4.9b

Counts

83 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x)))))))
28.1b	(sqrt (+ (* t t) (* l (/ l x))))
28.1b	(sqrt (+ (* t t) (* l (/ l x))))
28.1b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x))))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`sqrt-div`
36×	`associate-*r/`
16×	`flip3-+` `frac-add` `flip-+`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`frac-times`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 72

Calls

4 calls:

12.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x)))))))
4.0ms	(sqrt (+ (* t t) (* l (/ l x))))
4.0ms	(sqrt (+ (* t t) (* l (/ l x))))
14.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x))))))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x)))))))
14.0ms	(sqrt (+ (* t t) (* l (/ l x))))
14.0ms	(sqrt (+ (* t t) (* l (/ l x))))
25.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x))))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4978	2404
1	4978	2404

prune133.0ms

Filtered

65 candidates to 84 candidates (-29.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 4.9b

Counts

91 → 7

regimes310.0ms

Accuracy

76.1% (5.6b remaining)

Error of 10.2b against oracle of 4.5b and baseline of 28.2b

bsearch472.0ms

Steps

Iters	Range		Point
8	8.499686597203441e+36	6.71003475506411e+39	1.0144513413400185e+38
8	1.1005850145569503e-163	1.8372543573718782e-159	1.4464152816202683e-161
7	1.0525597551005402e-259	1.5754139860474638e-257	9.84043843066752e-258
10	-7.453171015441001e-208	-2.6210335470069818e-219	-1.7459689189787066e-212
11	-7.159577561379732e-109	-1.4678756255442547e-146	-1.4984775607051275e-146
7	-6.736503261442757e+153	-4.93123309422947e+151	-2.844712975366527e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	136	187
1	136	187

end0.0ms

sample2.9s

Algorithm

intervals

Results

648.0ms	9775×	body	80	nan
359.0ms	5062×	body	80	valid
295.0ms	890×	body	1280	valid
263.0ms	1013×	body	640	valid
183.0ms	576×	body	1280	nan
148.0ms	577×	body	640	nan
129.0ms	666×	body	320	valid
73.0ms	376×	body	320	nan
49.0ms	369×	body	160	valid
25.0ms	181×	body	160	nan

Details

sample108.0ms

simplify34.0ms

prune12.0ms

localize16.0ms

rewrite54.0ms

series345.0ms

simplify43.0ms

prune198.0ms

localize16.0ms

rewrite40.0ms

series53.0ms

simplify28.0ms

prune150.0ms

localize22.0ms

rewrite45.0ms

series55.0ms

simplify26.0ms

prune188.0ms

localize19.0ms

rewrite38.0ms

series70.0ms

simplify44.0ms

prune133.0ms

regimes310.0ms

bsearch472.0ms

simplify3.0ms

end0.0ms

sample2.9s

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