Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	453×	body	80	nan
18.0ms	290×	body	80	valid

simplify121.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.4b	(/ (* l l) Om)
13.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 141

Calls

4 calls:

45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0ms	(/ (* l l) Om)
124.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
96.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

386.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1176	2339
1	5001	2015

prune556.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.7b

localize23.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) 2.0))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

24.0ms	(* n (pow (/ l Om) 2.0))
46.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
126.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
95.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* n (pow (/ l Om) 2.0))
379.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1229	2457
1	5001	2136

prune596.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.2b

localize22.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.8b	(* n (pow (/ l Om) (/ 2.0 2)))
13.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
19.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 174

Calls

4 calls:

142.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
25.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
182.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
134.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series7.1s

Counts

4 → 12

Calls

4 calls:

391.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
178.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
5.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1355	3511
1	5002	2841

prune834.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize25.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
6.2b	(* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))
6.8b	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
19.8b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
31×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`add-cube-cbrt` `associate-l`
16×	`unpow-prod-down`
15×	`pow1`
10×	`times-frac` `cbrt-unprod`
7×	`pow-prod-down`
5×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
4×	`expm1-log1p-u` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `rem-sqrt-square` `flip3--` `associate-*r/` `div-exp` `flip--` `distribute-neg-frac` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-lft-neg-out` `neg-mul-1` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 118

Calls

4 calls:

27.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
62.0ms	(* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))
237.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
11.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

series11.7s

Counts

4 → 12

Calls

4 calls:

151.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
284.0ms	(* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))
1.1s	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
10.1s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U)) ( n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

simplify110.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	778	1678
1	3869	1454
2	5001	1445

prune536.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.2b

regimes603.0ms

Accuracy

25.1% (9.3b remaining)

Error of 28.2b against oracle of 18.9b and baseline of 31.4b

bsearch353.0ms

Steps

Iters	Range	Point
6	9.655969020719335e-299	8.902876449237102e-298	9.891457184010319e-299
9	-6.135579462598049e-178	-3.735328815158686e-183	-1.9843813902657215e-178
10	-4.595080940101684e-37	-3.0572799811341753e-49	-9.756238003230914e-48

Iters

Range

Point

9.655969020719335e-299

8.902876449237102e-298

9.891457184010319e-299

-6.135579462598049e-178

-3.735328815158686e-183

-1.9843813902657215e-178

-4.595080940101684e-37

-3.0572799811341753e-49

-9.756238003230914e-48

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	79
1	95	79
2	108	79
3	112	79
4	112	79

end0.0ms

sample2.8s

Algorithm

intervals

Results

924.0ms	14757×	body	80	nan
588.0ms	9196×	body	80	valid