Details

sample102.0ms

Algorithm

intervals

Results

16.0ms	360×	body	80	nan
8.0ms	158×	body	80	valid
7.0ms	40×	body	640	valid
7.0ms	27×	body	1280	valid
3.0ms	16×	body	1280	nan
3.0ms	20×	body	320	valid
3.0ms	15×	body	640	nan
2.0ms	12×	body	320	nan
1.0ms	11×	body	160	valid
1.0ms	8×	body	160	nan

simplify83.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize24.0ms

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)
15.4b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite142.0ms

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:

53.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms	(* (sqrt 2.0) t)
32.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
43.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

431.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
45.0ms	(* (sqrt 2.0) t)
223.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify65.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

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

prune293.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.5b

localize16.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.4b	(/ (pow l 2) x)
10.0b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite57.0ms

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:

18.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
11.0ms	(/ (pow l 2) x)
8.0ms	(/ (pow t 2) x)
16.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
165.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

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

prune421.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (/ l (/ x l)))
3.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
10.0b	(/ (pow t 2) x)
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite80.0ms

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:

32.0ms	(+ (pow t 2) (/ l (/ x l)))
17.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.0ms	(/ (pow t 2) x)
19.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (pow t 2) (/ l (/ x l)))
64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
24.0ms	(/ (pow t 2) x)
160.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	453	932
1	1835	862
2	5002	859

prune325.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize21.0ms

Local error

Found 4 expressions with local error:

10.0b	(/ (pow t 2) x)
26.1b	(sqrt (+ (pow t 2) (/ l (/ x l))))
26.1b	(sqrt (+ (pow t 2) (/ l (/ x l))))
26.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
11×	`sqrt-prod`
9×	`add-exp-log` `flip3-+` `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/` `distribute-lft-out`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

8.0ms	(/ (pow t 2) x)
55.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
57.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
27.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (pow t 2) x)
77.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
73.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
160.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	508	1356
1	1734	1296
2	5001	1291

prune378.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

regimes337.0ms

Accuracy

78.6% (5.0b remaining)

Error of 8.7b against oracle of 3.7b and baseline of 27.1b

bsearch344.0ms

Steps

Iters	Range		Point
2	4.3067122179417807e+123	4.913524705181093e+123	4.8376731442761786e+123
9	1.0846989892862971e-161	2.8171998045751283e-154	5.748160003020186e-158
6	4.682543563979993e-265	3.712032090684813e-264	2.5556856337554223e-264
10	-4.736252822648865e+153	-5.454035013448908e+141	-8.703772595808916e+141

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	107
1	84	107

end0.0ms

sample2.1s

Algorithm

intervals

Results

462.0ms	10138×	body	80	nan
254.0ms	5101×	body	80	valid
197.0ms	845×	body	1280	valid
194.0ms	1039×	body	640	valid
137.0ms	601×	body	1280	nan
106.0ms	600×	body	640	nan
92.0ms	677×	body	320	valid
42.0ms	328×	body	320	nan
31.0ms	338×	body	160	valid
16.0ms	183×	body	160	nan