Details

sample95.0ms

Algorithm

intervals

Results

18.0ms	358×	body	80	nan
14.0ms	9×	body	160	nan
9.0ms	172×	body	80	valid
9.0ms	29×	body	1280	valid
6.0ms	23×	body	1280	nan
6.0ms	28×	body	640	valid
5.0ms	25×	body	640	nan
2.0ms	14×	body	320	valid
2.0ms	14×	body	320	nan
1.0ms	13×	body	160	valid

simplify89.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 40.6b

Counts

2 → 1

localize18.0ms

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)
13.4b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.2b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

1110×	`add-sqr-sqrt`
504×	`sqrt-prod`
495×	`times-frac`
301×	`unswap-sqr`
298×	`*-un-lft-identity`
285×	`difference-of-squares`
238×	`associate-l`
146×	`add-cube-cbrt`
84×	`*-commutative`
81×	`associate-r`
76×	`distribute-lft-out--`
57×	`swap-sqr`
25×	`associate-/r*`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`sqrt-div` `associate--l+`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `div-inv`

Counts

4 → 548

Calls

4 calls:

94.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
75.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
80.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

434.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms	(* (sqrt 2.0) t)
222.0ms	(- (* (/ (+ 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)))

simplify221.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1111	13941
1	4267	13734
2	5001	13550

prune825.0ms

Filtered

560 candidates to 204 candidates (63.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	553	7	560
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	554	7	561

Merged error: 4.8b

Counts

561 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.7b	(/ (pow l 2) x)
10.2b	(/ (pow t 2) x)
25.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/`
71×	`*-un-lft-identity`
64×	`frac-add`
52×	`add-sqr-sqrt` `associate-/l*`
51×	`add-cube-cbrt`
48×	`times-frac`
36×	`unpow-prod-down`
34×	`flip3-+` `sqrt-div` `flip-+`
18×	`associate-/r*`
14×	`add-exp-log`
12×	`unpow2` `sqr-pow`
10×	`clear-num`
8×	`associate-l` `un-div-inv` `add-cbrt-cube` `distribute-lft-out`
7×	`sqrt-prod`
6×	`frac-2neg` `div-exp` `add-log-exp`
5×	`pow1`
4×	`associate-+r+`
3×	`+-commutative`
2×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 200

Calls

4 calls:

56.0ms	(+ (* 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)
56.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* 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)
172.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify134.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1026	3353
1	4672	3183
2	5002	3183

prune550.0ms

Filtered

212 candidates to 131 candidates (38.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	205	7	212
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	205	14	219

Merged error: 2.0b

Counts

219 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.2b	(/ (pow t 2) x)
25.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/`
64×	`frac-add`
57×	`*-un-lft-identity`
44×	`associate-/l*`
42×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
34×	`flip3-+` `sqrt-div` `flip-+`
24×	`unpow-prod-down` `times-frac`
15×	`associate-/r*`
14×	`associate-l`
11×	`add-exp-log` `sqrt-prod`
9×	`clear-num`
8×	`un-div-inv` `add-cbrt-cube` `distribute-lft-out` `unpow2` `sqr-pow`
7×	`pow1`
6×	`add-log-exp`
5×	`frac-2neg`
4×	`associate-+r+`
3×	`+-commutative` `div-exp` `associate-r`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 173

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
59.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.0ms	(/ (pow t 2) x)
57.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
68.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
26.0ms	(/ (pow t 2) x)
169.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify137.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	982	3150
1	4473	3050
2	5001	3050

prune475.0ms

Filtered

185 candidates to 113 candidates (38.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	185	14	199

Merged error: 2.0b

Counts

199 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (* l (/ l x)))
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.2b	(/ (pow t 2) x)
25.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/`
64×	`frac-add`
58×	`*-un-lft-identity`
44×	`associate-/l*`
35×	`add-sqr-sqrt` `flip3-+` `flip-+`
34×	`add-cube-cbrt` `sqrt-div`
24×	`unpow-prod-down` `times-frac`
15×	`associate-/r*`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-l` `clear-num`
8×	`un-div-inv` `unpow2` `add-log-exp` `sqr-pow`
7×	`sqrt-prod`
6×	`add-cbrt-cube`
5×	`pow1` `frac-2neg`
4×	`+-commutative` `associate-+r+`
3×	`div-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `sum-log`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`

Counts

4 → 164

Calls

4 calls:

15.0ms	(+ (pow t 2) (* l (/ l x)))
58.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.0ms	(/ (pow t 2) x)
58.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (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))))))

simplify127.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	959	3169
1	4154	3065
2	5001	3065

prune464.0ms

Filtered

176 candidates to 110 candidates (37.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	173	17	190

Merged error: 2.0b

Counts

190 → 17

regimes572.0ms

Accuracy

78% (5.3b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 27.6b

bsearch455.0ms

Steps

Iters	Range		Point
11	1.983077860352827e+74	1.2169948632822941e+95	1.1832275687710057e+95
10	-5.3392545773226386e-192	-6.0224735533564614e-204	-7.939779379132041e-199
4	-1.7040716024172982e-155	-1.0301582289462479e-155	-1.0512180218672182e-155
10	-6.413539866615064e+58	-1.0208429830464386e+44	-8.721903761098746e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	100
1	71	100

end0.0ms

sample2.1s

Algorithm

intervals

Results

518.0ms	10089×	body	80	nan
273.0ms	5160×	body	80	valid
215.0ms	829×	body	1280	valid
211.0ms	1052×	body	640	valid
152.0ms	605×	body	1280	nan
125.0ms	630×	body	640	nan
93.0ms	628×	body	320	valid
57.0ms	363×	body	320	nan
35.0ms	331×	body	160	valid
18.0ms	181×	body	160	nan