Details

analyze896.0ms

Algorithm: search

sample66.0ms

Algorithm

intervals

Results

11.0ms	165×	body	80	valid
9.0ms	22×	body	1280	nan
8.0ms	25×	body	1280	valid
7.0ms	29×	body	640	valid
6.0ms	25×	body	640	nan
4.0ms	22×	body	320	valid
3.0ms	47×	body	80	nan
2.0ms	11×	body	320	nan
2.0ms	15×	body	160	valid
1.0ms	4×	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: 40.3b

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))))
0.4b	(* (sqrt 2.0) t)
12.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite51.0ms

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:

15.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
5.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ 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)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t))))
4.0ms	(* (sqrt 2.0) t)
59.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
198.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify88.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (76.0ms)

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

prune275.0ms

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: 5.6b

Counts

115 → 7

localize19.0ms

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))))
5.7b	(/ (pow l 2) x)
8.3b	(/ (pow t 2) x)
24.1b	(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:

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)))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* 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)
26.0ms	(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

prune369.0ms

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: 3.3b

Counts

149 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (/ l (/ x l)))
2.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.3b	(/ (pow t 2) x)
24.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity` `times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
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` `distribute-lft-out`

Counts

4 → 93

Calls

4 calls:

22.0ms	(+ (pow t 2) (/ l (/ x l)))
9.0ms	(+ (* 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))))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (pow t 2) (/ l (/ x l)))
15.0ms	(+ (* 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))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	453	932
1	1835	862
2	5001	859

prune263.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	104	12	116

Merged error: 3.3b

Counts

116 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
2.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
8.3b	(/ (pow t 2) x)
24.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite31.0ms

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:

5.0ms	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
17.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
3.0ms	(/ (pow t 2) x)
33.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	503	1467
1	2109	1364
2	5001	1361

prune217.0ms

Filtered

77 candidates to 104 candidates (-35.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	104	12	116

Merged error: 3.3b

Counts

116 → 12

regimes615.0ms

Accuracy

77% (5.4b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 27.1b

bsearch768.0ms

Steps

Iters	Range		Point
6	5.2994694639463726e+110	4.869185285998734e+111	1.1760272104889051e+111
10	-5.671879865461847e+139	-6.431605247935335e+126	-9.501767693111941e+126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	57
1	59	57

end0.0ms

analyze751.0ms

Algorithm: search

sample1.9s

Algorithm

intervals

Results

355.0ms	5065×	body	80	valid
293.0ms	905×	body	1280	valid
260.0ms	1015×	body	640	valid
174.0ms	551×	body	1280	nan
139.0ms	544×	body	640	nan
133.0ms	666×	body	320	valid
94.0ms	1419×	body	80	nan
70.0ms	374×	body	320	nan
48.0ms	349×	body	160	valid
27.0ms	196×	body	160	nan

Details

analyze896.0ms

sample66.0ms

simplify79.0ms

prune4.0ms

localize16.0ms

rewrite51.0ms

series292.0ms

simplify88.0ms

prune275.0ms

localize19.0ms

rewrite31.0ms

series51.0ms

simplify63.0ms

prune369.0ms

localize16.0ms

rewrite46.0ms

series53.0ms

simplify57.0ms

prune263.0ms

localize21.0ms

rewrite31.0ms

series66.0ms

simplify65.0ms

prune217.0ms

regimes615.0ms

bsearch768.0ms

simplify2.0ms

end0.0ms

analyze751.0ms

sample1.9s

Profiling