Details

sample82.0ms

Algorithm

intervals

Results

15.0ms	310×	body	80	nan
9.0ms	167×	body	80	valid
6.0ms	32×	body	640	valid
6.0ms	25×	body	1280	valid
5.0ms	19×	body	1280	nan
3.0ms	15×	body	640	nan
2.0ms	17×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	10×	body	320	nan
0.0ms	5×	body	160	nan

simplify88.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize19.0ms

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)
12.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite52.0ms

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))))
4.0ms	(* (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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

429.0ms	(/ (* (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)
217.0ms	(- (* (/ (+ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	417	1208
1	2051	1099
2	5002	1094

prune306.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.1b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
27.6b	(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)))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
24.0ms	(/ (pow t 2) x)
170.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (51.0ms)

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

prune478.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
4.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.5b	(/ (pow t 2) x)
27.6b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite62.0ms

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:

39.0ms	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
23.0ms	(/ (pow t 2) x)
163.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	456	1099
1	1941	1003
2	5003	982

prune402.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (* l (/ l x)))
4.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
9.5b	(/ (pow t 2) x)
27.6b	(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:

4.0ms	(+ (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))))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (pow t 2) (* l (/ l x)))
69.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
19.0ms	(/ (pow t 2) x)
172.0ms	(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 (48.0ms)

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

prune319.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

regimes557.0ms

Accuracy

73.9% (6.2b remaining)

Error of 10.0b against oracle of 3.8b and baseline of 27.4b

bsearch421.0ms

Steps

Iters	Range		Point
7	2.896305437726327e+111	1.3118630056926933e+113	1.2953282500941115e+113
4	-2.0786106758946992e-238	-1.3297541091157469e-238	-1.4640217334256062e-238
9	-1.6835204431162708e-199	-2.9969892637229514e-206	-2.958463792680025e-203
9	-1.7953405712417382e-26	-1.5166399548635069e-33	-1.7657799131066967e-26

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	94
1	70	94
2	70	94

end0.0ms

sample2.1s

Algorithm

intervals

Results

511.0ms	10275×	body	80	nan
259.0ms	5099×	body	80	valid
216.0ms	878×	body	1280	valid
203.0ms	1040×	body	640	valid
144.0ms	596×	body	1280	nan
119.0ms	616×	body	640	nan
86.0ms	593×	body	320	valid
53.0ms	367×	body	320	nan
38.0ms	390×	body	160	valid
17.0ms	181×	body	160	nan