Details

sample101.0ms

Algorithm

intervals

Results

20.0ms	299×	body	80	nan
13.0ms	38×	body	1280	valid
11.0ms	166×	body	80	valid
8.0ms	12×	body	320	nan
8.0ms	29×	body	640	valid
7.0ms	22×	body	1280	nan
6.0ms	22×	body	640	nan
2.0ms	11×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify89.0ms

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: 42.2b

Counts

2 → 1

localize25.0ms

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)
14.9b	(- (* (/ (+ 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)))

rewrite53.0ms

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:

422.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms	(* (sqrt 2.0) t)
211.0ms	(- (* (/ (+ 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	1208
1	2051	1099
2	5002	1094

prune293.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 7.1b

Counts

93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.4b	(/ (pow l 2) x)
9.3b	(/ (pow t 2) x)
27.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite35.0ms

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)))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
24.0ms	(/ (pow t 2) x)
156.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (51.0ms)

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

prune421.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Merged error: 4.9b

Counts

148 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (* l (/ l x)))
4.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.3b	(/ (pow t 2) x)
27.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite28.0ms

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) (* l (/ l x)))
9.0ms	(+ (* 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))))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (pow t 2) (* l (/ l x)))
67.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	456	925
1	1936	858
2	5001	855

prune315.0ms

Filtered

104 candidates to 75 candidates (72.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	103	13	116

Merged error: 4.9b

Counts

116 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
4.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
9.3b	(/ (pow t 2) x)
27.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

rewrite32.0ms

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))))
9.0ms	(+ (* 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)))))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))
66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x))))))
22.0ms	(/ (pow t 2) x)
156.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (/ (fabs l) (cbrt x)) (cbrt x)) (/ (fabs l) (cbrt x)))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	499	1468
1	2115	1360
2	5002	1357

prune340.0ms

Filtered

104 candidates to 77 candidates (74.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	103	14	117

Merged error: 4.9b

Counts

117 → 14

regimes471.0ms

Accuracy

78.4% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 28.0b

bsearch114.0ms

Steps

Iters	Range		Point
7	2.428002561672062e+78	5.363859432985812e+80	1.1269602960894555e+80
1	-4.3651366941439665e+140	-3.967062851698274e+140	-4.066581312309697e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	57
1	60	57

end0.0ms

sample2.7s

Algorithm

intervals

Results

673.0ms	9985×	body	80	nan
348.0ms	5101×	body	80	valid
302.0ms	909×	body	1280	valid
259.0ms	989×	body	640	valid
197.0ms	597×	body	1280	nan
160.0ms	616×	body	640	nan
125.0ms	631×	body	320	valid
68.0ms	326×	body	320	nan
48.0ms	370×	body	160	valid
25.0ms	200×	body	160	nan

Details

sample101.0ms

simplify89.0ms

prune5.0ms

localize25.0ms

rewrite53.0ms

series1.8s

simplify63.0ms

prune293.0ms

localize16.0ms

rewrite35.0ms

series263.0ms

simplify64.0ms

prune421.0ms

localize19.0ms

rewrite28.0ms

series281.0ms

simplify61.0ms

prune315.0ms

localize20.0ms

rewrite32.0ms

series290.0ms

simplify66.0ms

prune340.0ms

regimes471.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling