Details

sample72.0ms

Algorithm

intervals

Results

14.0ms	276×	body	80	nan
8.0ms	42×	body	640	valid
8.0ms	31×	body	1280	valid
8.0ms	147×	body	80	valid
4.0ms	24×	body	320	valid
3.0ms	14×	body	1280	nan
3.0ms	15×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	5×	body	160	nan

simplify97.0ms

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: 44.8b

Counts

2 → 1

localize27.0ms

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))))
0.4b	(* (sqrt 2.0) t)
14.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

16.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

425.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms	(* (sqrt 2.0) t)
217.0ms	(- (* (/ (+ 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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	446	1290
1	2206	1177
2	5002	1172

prune343.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Merged error: 6.4b

Counts

103 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.6b	(/ (pow l 2) x)
10.3b	(/ (pow t 2) x)
27.5b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(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)
271.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	377	811
1	1351	724
2	5001	715

prune459.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	129	10	139
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	131	14	145

Merged error: 3.7b

Counts

145 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
4.0b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.3b	(/ (pow t 2) x)
27.5b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt 2.0) t)
66.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
259.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	321	666
1	1291	592
2	5001	586

prune348.0ms

Filtered

112 candidates to 77 candidates (68.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	111	15	126

Merged error: 3.7b

Counts

126 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
4.0b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.3b	(/ (pow t 2) x)
27.5b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
14×	`add-exp-log`
12×	`unpow-prod-down` `sqrt-prod`
11×	`add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

9.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
5.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
62.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
23.0ms	(/ (pow t 2) x)
258.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	358	733
1	1338	640
2	5002	630

prune333.0ms

Filtered

114 candidates to 79 candidates (69.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	112	17	129

Merged error: 3.7b

Counts

129 → 17

regimes706.0ms

Accuracy

75.8% (5.6b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 27.3b

bsearch468.0ms

Steps

Iters	Range		Point
10	8.080361795648996e+113	9.444791583695139e+125	1.0129885136066577e+120
7	6.604386851469226e-290	1.0414459619351038e-287	7.335765889311208e-290
10	-3.981060198628893e-302	5.4468660893141494e-304	5.380647169889281e-304
8	-1.4947697976536127e+105	-4.072858663264593e+102	-1.0993530493582173e+103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	67
1	62	67

end0.0ms

sample2.1s

Algorithm

intervals

Results

501.0ms	10141×	body	80	nan
258.0ms	5032×	body	80	valid
231.0ms	903×	body	1280	valid
201.0ms	1030×	body	640	valid
155.0ms	628×	body	1280	nan
124.0ms	605×	body	640	nan
100.0ms	687×	body	320	valid
48.0ms	334×	body	320	nan
37.0ms	348×	body	160	valid
17.0ms	173×	body	160	nan