Details

sample88.0ms

Algorithm

intervals

Results

12.0ms	173×	body	80	valid
12.0ms	172×	body	80	nan
11.0ms	33×	body	1280	valid
9.0ms	32×	body	640	valid
6.0ms	25×	body	640	nan
6.0ms	17×	body	1280	nan
3.0ms	16×	body	320	valid
3.0ms	16×	body	320	nan
0.0ms	3×	body	160	nan
0.0ms	2×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 41.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
0.5b	(* (sqrt 2.0) t)
9.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`sqrt-prod`
6×	`associate-r` `add-log-exp`
5×	`distribute-lft-out`
4×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `associate-r/` `pow-prod-down` `associate--l+` `associate-/r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 102

Calls

4 calls:

14.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
4.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
12.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
4.0ms	(* (sqrt 2.0) t)
56.0ms	(- (* (/ (+ 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)))

simplify90.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	700	1206
1	3840	1127
2	5001	1126

prune263.0ms

Filtered

81 candidates to 114 candidates (-40.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 7.0b

Counts

115 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (pow l 2) x)
5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
9.5b	(/ (pow t 2) x)
28.2b	(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:

7.0ms	(/ (pow l 2) x)
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (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)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (pow l 2) x)
15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune349.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Merged error: 4.5b

Counts

149 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite27.0ms

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:

4.0ms	(* (sqrt 2.0) t)
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
16.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms	(/ (pow t 2) x)
24.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	477	917
1	2140	851
2	5001	848

prune258.0ms

Filtered

80 candidates to 115 candidates (-43.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	115	11	126

Merged error: 4.5b

Counts

126 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
5.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.5b	(/ (pow t 2) x)
28.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

8.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
16.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	517	989
1	2133	891
2	5001	884

prune267.0ms

Filtered

81 candidates to 117 candidates (-44.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	115	13	128

Merged error: 4.5b

Counts

128 → 13

regimes760.0ms

Accuracy

74.6% (6.1b remaining)

Error of 10.0b against oracle of 3.9b and baseline of 28.0b

bsearch491.0ms

Steps

Iters	Range		Point
10	1.3803164574196006e+139	1.7655636947019656e+149	4.820042214716454e+142
8	1.5221367998880468e-155	3.1133396657127777e-152	1.5421627121715643e-155
9	4.226098096886031e-301	2.9998909454411807e-292	6.144838275917855e-294
9	-5.537880763075817e-290	-9.411929643985496e-296	-2.3901519997553357e-290
8	-1.4211525735560003e-240	-3.408512747575795e-245	-5.018414545278973e-245
7	-2.641920954763069e+120	-1.466337608653382e+118	-4.834513696311149e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	135
1	83	135
2	86	135
3	86	135

end0.0ms

sample2.4s

Algorithm

intervals

Results

368.0ms	5101×	body	80	valid
363.0ms	5261×	body	80	nan
293.0ms	857×	body	1280	valid
274.0ms	1045×	body	640	valid
216.0ms	648×	body	1280	nan
157.0ms	591×	body	640	nan
135.0ms	655×	body	320	valid
67.0ms	339×	body	320	nan
46.0ms	342×	body	160	valid
25.0ms	174×	body	160	nan

Details

sample88.0ms

simplify78.0ms

prune4.0ms

localize16.0ms

rewrite46.0ms

series282.0ms

simplify90.0ms

prune263.0ms

localize16.0ms

rewrite31.0ms

series46.0ms

simplify61.0ms

prune349.0ms

localize16.0ms

rewrite27.0ms

series48.0ms

simplify62.0ms

prune258.0ms

localize18.0ms

rewrite31.0ms

series48.0ms

simplify63.0ms

prune267.0ms

regimes760.0ms

bsearch491.0ms

simplify3.0ms

end0.0ms

sample2.4s

Profiling