Details

sample110.0ms

Algorithm

intervals

Results

23.0ms	320×	body	80	nan
23.0ms	28×	body	1280	valid
12.0ms	166×	body	80	valid
10.0ms	35×	body	640	valid
7.0ms	21×	body	1280	nan
4.0ms	15×	body	640	nan
3.0ms	15×	body	320	valid
2.0ms	10×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune5.0ms

Filtered

1 candidates to 0 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: 43.4b

Counts

2 → 1

localize24.0ms

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)
14.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.4b	(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 → 80

Calls

4 calls:

17.0ms	(/ (* (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)
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)))

series1.8s

Counts

4 → 12

Calls

4 calls:

418.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms	(* (sqrt 2.0) t)
212.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify63.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune290.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 7.8b

Counts

93 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.6b	(/ (pow l 2) x)
9.4b	(/ (pow t 2) x)
26.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

10.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
23.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
164.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	526	1093
1	2235	984
2	5001	978

prune418.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	134	13	147

Merged error: 4.2b

Counts

147 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.4b	(/ (pow t 2) x)
26.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `add-cbrt-cube` `associate-/l`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`associate-+r+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
12.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sqrt 2.0) t)
61.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
23.0ms	(/ (pow t 2) x)
157.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	478	914
1	2189	851
2	5001	848

prune324.0ms

Filtered

115 candidates to 79 candidates (68.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	4	7	11
Picked	0	1	1
Done	0	1	1
Total	116	12	128

Merged error: 4.2b

Counts

128 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.4b	(/ (pow t 2) x)
26.4b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
16×	`cbrt-prod`
12×	`pow1` `unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `associate-/l`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `unswap-sqr` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`associate-+r+` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`cbrt-undiv` `+-commutative` `pow2` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 121

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
12.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (cbrt x) (cbrt x))
84.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms	(/ (pow t 2) x)
181.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	520	1310
1	2335	1209
2	5001	1186

prune390.0ms

Filtered

133 candidates to 91 candidates (68.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	133	12	145

Merged error: 4.2b

Counts

145 → 12

regimes520.0ms

Accuracy

76.4% (5.6b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 27.5b

bsearch478.0ms

Steps

Iters	Range		Point
7	1.8409252909116086e+140	3.646962701262837e+141	1.9351646333110816e+140
9	-1.2785095843447461e-272	-1.559109080965685e-277	-4.446639441849728e-275
7	-2.847866590662546e-207	-1.601756126752375e-209	-3.697780864525128e-209
7	-2.256807204228932e+50	-5.421158016186142e+48	-1.4184858308600574e+50

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	92
1	66	92

end0.0ms

sample2.7s

Algorithm

intervals

Results

676.0ms	9915×	body	80	nan
354.0ms	5107×	body	80	valid
272.0ms	1029×	body	640	valid
271.0ms	792×	body	1280	valid
199.0ms	597×	body	1280	nan
154.0ms	589×	body	640	nan
140.0ms	672×	body	320	valid
72.0ms	365×	body	320	nan
53.0ms	400×	body	160	valid
25.0ms	190×	body	160	nan

Details

sample110.0ms

simplify87.0ms

prune5.0ms

localize24.0ms

rewrite52.0ms

series1.8s

simplify63.0ms

prune290.0ms

localize17.0ms

rewrite31.0ms

series267.0ms

simplify69.0ms

prune418.0ms

localize16.0ms

rewrite32.0ms

series284.0ms

simplify66.0ms

prune324.0ms

localize20.0ms

rewrite34.0ms

series484.0ms

simplify72.0ms

prune390.0ms

regimes520.0ms

bsearch478.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling