Details

sample893.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0.017926%

Results

23.0ms	337×	body	80	nan
12.0ms	166×	body	80	valid
12.0ms	35×	body	1280	valid
10.0ms	28×	body	640	valid
6.0ms	19×	body	1280	nan
5.0ms	20×	body	640	nan
4.0ms	20×	body	320	valid
2.0ms	12×	body	320	nan
1.0ms	7×	body	160	valid
1.0ms	5×	body	160	nan

simplify80.0ms

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: 42.7b

Counts

2 → 1

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)
13.5b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite46.0ms

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:

16.0ms	(/ (* (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)
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)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* (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))
194.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (46.0ms)

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

prune211.0ms

Filtered

65 candidates to 92 candidates (-41.5%)

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: 5.8b

Counts

93 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.4b	(/ (pow l 2) x)
9.9b	(/ (pow t 2) x)
26.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

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:

9.0ms	(+ (* 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)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow l 2) x)
6.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

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

prune372.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	136	11	147

Merged error: 3.5b

Counts

147 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
2.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.9b	(/ (pow t 2) x)
26.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite30.0ms

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)
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

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

prune269.0ms

Filtered

79 candidates to 115 candidates (-45.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 3.5b

Counts

126 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (* l (/ l x)))
2.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.9b	(/ (pow t 2) x)
26.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

4.0ms	(+ (pow t 2) (* l (/ l x)))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (pow t 2) (* l (/ l x)))
15.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms	(/ (pow t 2) x)
25.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	456	925
1	1936	858
2	5003	855

prune312.0ms

Filtered

75 candidates to 104 candidates (-38.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 3.5b

Counts

114 → 12

regimes1.1s

Accuracy

77.6% (5.4b remaining)

Error of 9.2b against oracle of 3.8b and baseline of 27.9b

bsearch282.0ms

Steps

Iters	Range		Point
8	1.0686265415311349e+133	2.3546588527009796e+137	1.671565982166491e+133
7	-3.4737201751485775e-227	-1.7990754188899262e-229	-3.411433639833263e-227
10	-4.125709241753314e-155	-6.204707435563575e-167	-4.757165686163845e-158
8	-5.938723479847873e+78	-8.923302015283854e+75	-6.99384236621146e+77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	99
1	82	99

end0.0ms

sample3.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0.017926%

Results

685.0ms	9914×	body	80	nan
377.0ms	5089×	body	80	valid
312.0ms	912×	body	1280	valid
262.0ms	976×	body	640	valid
179.0ms	531×	body	1280	nan
167.0ms	622×	body	640	nan
133.0ms	660×	body	320	valid
67.0ms	336×	body	320	nan
50.0ms	363×	body	160	valid
24.0ms	179×	body	160	nan

Details

sample893.0ms

simplify80.0ms

prune4.0ms

localize16.0ms

rewrite46.0ms

series349.0ms

simplify60.0ms

prune211.0ms

localize17.0ms

rewrite30.0ms

series50.0ms

simplify63.0ms

prune372.0ms

localize16.0ms

rewrite30.0ms

series48.0ms

simplify66.0ms

prune269.0ms

localize19.0ms

rewrite29.0ms

series52.0ms

simplify58.0ms

prune312.0ms

regimes1.1s

bsearch282.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling