Details

sample376.0ms

Algorithm

intervals

Results

62.0ms	546×	body	80	nan
27.0ms	295×	body	80	valid

simplify132.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

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: 36.5b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

5.9b	(* n (pow (/ l Om) 2.0))
8.2b	(/ (* l l) Om)
13.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-exp-log`
23×	`pow1`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`prod-diff` `pow-prod-down`
11×	`prod-exp`
10×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 132

Calls

4 calls:

17.0ms	(* n (pow (/ l Om) 2.0))
5.0ms	(/ (* l l) Om)
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
15.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

144.0ms	(* n (pow (/ l Om) 2.0))
19.0ms	(/ (* l l) Om)
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(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

144 → 144

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1079	1952
1	5001	1746

prune561.0ms

Filtered

144 candidates to 99 candidates (68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	131	13	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Merged error: 19.1b

Counts

145 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.9b	(* n (pow (/ l Om) 2.0))
13.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.6b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`prod-diff`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-*r/`
23×	`pow1`
22×	`associate--r+`
21×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
20×	`associate-r`
15×	`unpow-prod-down` `flip3--` `associate--l+` `add-cbrt-cube` `flip--`
12×	`pow-prod-down` `frac-sub`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
8×	`sub-neg`
7×	`cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 162

Calls

4 calls:

14.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
9.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(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:

675.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
144.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1246	2749
1	5001	2446

prune665.0ms

Filtered

174 candidates to 125 candidates (71.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	169	5	174
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	175	12	187

Merged error: 17.9b

Counts

187 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.9b	(* n (pow (/ l Om) 2.0))
7.9b	(* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) U))
16.6b	(sqrt (* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) U)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
24×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`associate-r` `add-cbrt-cube`
16×	`pow-prod-down`
15×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`prod-exp`
10×	`times-frac`
9×	`cbrt-unprod`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `associate-r/` `associate-l` `associate-l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`flip3--` `sqrt-div` `pow-exp` `*-commutative` `flip--` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
14.0ms	(* n (pow (/ l Om) 2.0))
9.0ms	(* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) U))
7.0ms	(sqrt (* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) U)))

series12.5s

Counts

4 → 12

Calls

4 calls:

316.0ms	(fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
151.0ms	(* n (pow (/ l Om) 2.0))
992.0ms	(* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) U))
11.1s	(sqrt (* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) U)))

simplify81.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	631	1147
1	2778	994
2	5002	992

prune415.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Merged error: 16.2b

Counts

117 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
4.9b	(* n (pow (/ l Om) (/ 2.0 2)))
7.9b	(* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) U))
16.6b	(sqrt (* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) U)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
24×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`associate-r` `add-cbrt-cube`
16×	`pow-prod-down`
15×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`prod-exp`
10×	`times-frac`
9×	`cbrt-unprod`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `associate-r/` `associate-l` `associate-l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`flip3--` `sqrt-div` `pow-exp` `*-commutative` `flip--` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
9.0ms	(* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) U))
7.0ms	(sqrt (* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) U)))

series12.6s

Counts

4 → 12

Calls

4 calls:

293.0ms	(fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
156.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
939.0ms	(* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) U))
11.2s	(sqrt (* (* 2.0 n) (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) U)))

simplify78.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	655	1531
1	2854	1295
2	5002	1281

prune346.0ms

Filtered

105 candidates to 77 candidates (73.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	105	12	117

Merged error: 16.2b

Counts

117 → 12

regimes469.0ms

Accuracy

9.5% (10.8b remaining)

Error of 29.5b against oracle of 18.7b and baseline of 30.7b

bsearch282.0ms

Steps

Iters	Range	Point
7	3.921037642294131e+125	1.740091957814032e+127	1.2741787044483237e+126
6	1.4271352254573342e-194	1.0361376704456973e-193	7.068245229557905e-194
6	4.3236642318716767e-278	2.1777929378670944e-277	1.9876102665034602e-277

Iters

Range

Point

3.921037642294131e+125

1.740091957814032e+127

1.2741787044483237e+126

1.4271352254573342e-194

1.0361376704456973e-193

7.068245229557905e-194

4.3236642318716767e-278

2.1777929378670944e-277

1.9876102665034602e-277

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	61
1	63	61

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	14999×	body	80	nan
787.0ms	9154×	body	80	valid