Details

sample357.0ms

Algorithm

intervals

Results

41.0ms	521×	body	80	nan
23.0ms	299×	body	80	valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize22.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9b	(/ (* l l) Om)
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(/ (* l l) Om)
126.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
85.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series5.9s

Counts

4 → 12

Calls

4 calls:

333.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
16.0ms	(/ (* l l) Om)
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify122.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	937	1544
1	4764	1385
2	5001	1385

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.6b

localize20.0ms

Local error

Found 4 expressions with local error:

6.3b	(* n (pow (/ l Om) 2.0))
7.3b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 119

Calls

4 calls:

25.0ms	(* n (pow (/ l Om) 2.0))
44.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
126.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
82.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.0s

Counts

4 → 12

Calls

4 calls:

134.0ms	(* n (pow (/ l Om) 2.0))
327.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.3s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.9b

localize22.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) (/ 2.0 2)))
7.3b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `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 → 136

Calls

4 calls:

26.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
142.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
181.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
119.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

150.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
327.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5002	2030

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.9b

localize25.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (pow (/ l Om) (/ 2.0 2)) n)
7.3b	(* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
19×	`associate-l`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `associate-r` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 136

Calls

4 calls:

26.0ms	(* (pow (/ l Om) (/ 2.0 2)) n)
141.0ms	(* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*))
184.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
119.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (pow (/ l Om) (/ 2.0 2)) n)
379.0ms	(* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1076	2407
1	4981	2117
2	5001	2117

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.2b

regimes1.1s

Accuracy

9.6% (9.1b remaining)

Error of 30.7b against oracle of 21.6b and baseline of 31.7b

bsearch268.0ms

Steps

Iters	Range		Point
7	2.2616196897616447e-241	9.238327995984432e-240	1.3326251204934962e-240
5	-4.992339190090422e+36	-1.6116736530450838e+36	-1.9921574548518883e+36

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	56
1	73	56
2	74	56
3	74	56

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	15021×	body	80	nan
688.0ms	9142×	body	80	valid