Details

sample91.0ms

Algorithm

intervals

Results

21.0ms	155×	body	80	valid
17.0ms	308×	body	80	nan
8.0ms	38×	body	640	valid
7.0ms	23×	body	1280	valid
4.0ms	16×	body	1280	nan
3.0ms	21×	body	320	valid
3.0ms	12×	body	640	nan
2.0ms	19×	body	160	valid
2.0ms	11×	body	320	nan
1.0ms	5×	body	160	nan

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	14
1	101	14
2	234	14
3	525	14
4	1016	14
5	1701	14
6	3626	14
7	5002	14

prune5.0ms

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: 45.3b

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)
15.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`prod-diff` `*-commutative`
9×	`associate-l`
8×	`associate-/r/`
6×	`flip3--` `flip--`
5×	`fma-neg`
4×	`sqrt-div` `associate--l+` `div-inv`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-/l*`
1×	`sub-neg` `frac-2neg` `pow1/2` `clear-num`

Counts

4 → 34

Calls

4 calls:

24.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
3.0ms	(* (sqrt 2.0) t)
14.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

420.0ms	(/ (* (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)
212.0ms	(- (* (/ (+ 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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	358	544
1	1425	519
2	5001	496

prune158.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	40	6	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	6	47

Merged error: 6.9b

Counts

47 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.4b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
30.4b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-/l*`
2×	`frac-2neg` `clear-num` `div-inv` `unpow2` `sqr-pow`
1×	`pow1/2` `fma-udef`

Counts

4 → 12

Calls

4 calls:

1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
3.0ms	(/ (pow l 2) x)
3.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
265.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	108	78
1	337	77
2	1186	74
3	5002	69

prune84.0ms

Filtered

24 candidates to 16 candidates (66.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	23	7	30

Merged error: 4.4b

Counts

30 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
5.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
9.5b	(/ (pow t 2) x)
30.4b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-/l*`
1×	`frac-2neg` `pow1/2` `clear-num` `*-commutative` `fma-udef` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 8

Calls

4 calls:

3.0ms	(* (sqrt 2.0) t)
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
3.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
69.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
263.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l (/ 2 2)) (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	101	70
1	298	69
2	1051	66
3	3877	61
4	5001	61

prune67.0ms

Filtered

20 candidates to 12 candidates (60.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	20	7	27

Merged error: 4.4b

Counts

27 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
0.9b	(/ 2.0 (pow x 2))
1.0b	(pow (sqrt 2.0) 3)
9.0b	(* (/ 2.0 (pow x 2)) (- (/ t (pow (sqrt 2.0) 3)) (/ t (sqrt 2.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

90×	`frac-times` `frac-sub`
82×	`associate-/r*`
68×	`frac-2neg` `clear-num`
39×	`sqr-pow`
25×	`unpow3`
20×	`unpow2`
18×	`associate-*r/`
8×	`div-inv`
6×	`flip3--` `flip--` `sub-div`
5×	`associate-*l/`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `prod-diff` `*-commutative`
1×	`pow-to-exp` `pow-pow` `pow1/2` `associate-r` `associate-l` `sqrt-pow2` `distribute-lft-out--`

Counts

4 → 133

Calls

4 calls:

3.0ms	(* (sqrt 2.0) t)
2.0ms	(/ 2.0 (pow x 2))
2.0ms	(pow (sqrt 2.0) 3)
13.0ms	(* (/ 2.0 (pow x 2)) (- (/ t (pow (sqrt 2.0) 3)) (/ t (sqrt 2.0))))

series359.0ms

Counts

4 → 10

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
29.0ms	(/ 2.0 (pow x 2))
0.0ms	(pow (sqrt 2.0) 3)
291.0ms	(* (/ 2.0 (pow x 2)) (- (/ t (pow (sqrt 2.0) 3)) (/ t (sqrt 2.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1040	1807
1	5001	1688

prune441.0ms

Filtered

143 candidates to 98 candidates (68.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	143	7	150

Merged error: 4.4b

Counts

150 → 7

regimes363.0ms

Accuracy

74.4% (6.1b remaining)

Error of 9.8b against oracle of 3.7b and baseline of 27.6b

bsearch613.0ms

Steps

Iters	Range		Point
8	3.403568998745067e+87	4.905813436801621e+90	4.488332034392144e+90
8	1.7245540549261378e-174	7.545122391836811e-171	4.899761605523815e-171
10	3.871683063339351e-223	9.005404400815374e-213	6.311404485509687e-213
4	-6.914198310900146e-265	-3.618629021631408e-265	-6.769228911391228e-265
8	-9.505671634543452e-166	-2.1070939213285662e-168	-9.359052842342105e-167
6	-31565395626.252914	-3186624082.971198	-31115301794.108517

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	118
1	78	118

end0.0ms

sample2.2s

Algorithm

intervals

Results

555.0ms	10323×	body	80	nan
282.0ms	5047×	body	80	valid
245.0ms	903×	body	1280	valid
224.0ms	1044×	body	640	valid
156.0ms	598×	body	1280	nan
125.0ms	604×	body	640	nan
101.0ms	635×	body	320	valid
54.0ms	335×	body	320	nan
40.0ms	371×	body	160	valid
20.0ms	188×	body	160	nan