Details

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 27.647569%

Results

12.0ms	163×	body	80	valid
10.0ms	36×	body	640	valid
9.0ms	27×	body	1280	valid
7.0ms	28×	body	640	nan
7.0ms	21×	body	1280	nan
4.0ms	53×	body	80	nan
3.0ms	15×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	9×	body	320	nan
1.0ms	10×	body	160	nan

simplify79.0ms

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: 42.6b

Counts

2 → 1

localize17.0ms

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)
12.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite47.0ms

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))))
5.0ms	(* (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)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (* (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)
56.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
185.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify58.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (46.0ms)

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

prune197.0ms

Filtered

65 candidates to 92 candidates (-41.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Merged error: 5.5b

Counts

93 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0b	(/ (pow l 2) x)
8.5b	(/ (pow t 2) x)
27.2b	(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)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (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)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

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

prune338.0ms

Filtered

97 candidates to 142 candidates (-46.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Merged error: 3.8b

Counts

146 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* l (/ l x)))
2.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
8.5b	(/ (pow t 2) x)
27.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite27.0ms

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

series53.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (pow t 2) (* l (/ l x)))
14.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms	(/ (pow t 2) x)
24.0ms	(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

prune248.0ms

Filtered

75 candidates to 104 candidates (-38.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Merged error: 3.8b

Counts

111 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

8.5b	(/ (pow t 2) x)
26.9b	(sqrt (+ (pow t 2) (* l (/ l x))))
26.9b	(sqrt (+ (pow t 2) (* l (/ l x))))
27.2b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
9×	`add-exp-log` `flip3-+` `sqrt-prod` `flip-+`
8×	`frac-add` `associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`frac-times` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
2×	`associate-*l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (pow t 2) x)
19.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
16.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
26.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	507	1342
1	1757	1284
2	5003	1281

prune302.0ms

Filtered

83 candidates to 114 candidates (-37.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	114	8	122

Merged error: 3.8b

Counts

122 → 8

regimes663.0ms

Accuracy

76.1% (5.8b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 28.1b

bsearch500.0ms

Steps

Iters	Range		Point
9	2.8848128857044072e+72	3.4880343681095167e+81	2.9843805005488113e+81
6	4.817644149547986e-204	3.606260753334598e-203	6.047313775078897e-204
9	6.0703515302714085e-248	1.4315270014288731e-241	3.3270366640675283e-243
9	-1.378344997610523e-298	-4.5276047902380953e-305	-1.3583216648888047e-298
6	-1.8665996155531805e-240	-1.4446306504137724e-241	-1.7722596374613524e-241
9	-1.6344916224392814e+32	-4.087576932918366e+26	-6.680230459572395e+30

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	134
1	83	134

end0.0ms

sample5.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 27.647569%

Results

390.0ms	5185×	body	80	valid
303.0ms	859×	body	1280	valid
274.0ms	997×	body	640	valid
206.0ms	606×	body	1280	nan
159.0ms	588×	body	640	nan
128.0ms	634×	body	320	valid
101.0ms	1453×	body	80	nan
70.0ms	353×	body	320	nan
46.0ms	325×	body	160	valid
25.0ms	188×	body	160	nan

Details

sample3.0s

simplify79.0ms

prune4.0ms

localize17.0ms

rewrite47.0ms

series333.0ms

simplify58.0ms

prune197.0ms

localize18.0ms

rewrite30.0ms

series45.0ms

simplify66.0ms

prune338.0ms

localize18.0ms

rewrite27.0ms

series53.0ms

simplify58.0ms

prune248.0ms

localize19.0ms

rewrite28.0ms

series64.0ms

simplify58.0ms

prune302.0ms

regimes663.0ms

bsearch500.0ms

simplify3.0ms

end0.0ms

sample5.0s

Profiling