Details

sample101.0ms

Algorithm

intervals

Results

33.0ms	358×	body	80	nan
10.0ms	172×	body	80	valid
8.0ms	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
2.0ms	9×	body	160	nan
1.0ms	13×	body	160	valid

simplify99.0ms

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 (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

localize20.0ms

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)))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

1790×	`add-sqr-sqrt`
1106×	`*-un-lft-identity`
838×	`associate-l`
831×	`times-frac`
600×	`prod-diff`
538×	`add-cube-cbrt`
504×	`sqrt-prod`
373×	`unswap-sqr`
349×	`difference-of-squares`
313×	`associate-r`
177×	`swap-sqr`
144×	`distribute-lft-out`
140×	`*-commutative` `distribute-lft-out--`
40×	`fma-neg`
34×	`associate-/r/`
25×	`associate-/r*`
19×	`flip3--` `flip--`
17×	`div-inv`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate--l+` `log1p-expm1-u`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num`

Counts

4 → 1196

Calls

4 calls:

92.0ms	(/ (* (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)
86.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
117.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.0s

Counts

4 → 12

Calls

4 calls:

452.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms	(* (sqrt 2.0) t)
223.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.3s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify305.0ms

Algorithm

egg-herbie

Counts

1208 → 1208

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2189	28856
1	5002	26621

prune1.3s

Filtered

1208 candidates to 308 candidates (74.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1201	7	1208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1202	7	1209

Merged error: 4.8b

Counts

1209 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.7b	(/ (pow l 2) x)
10.2b	(/ (pow t 2) x)
25.0b	(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)))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow l 2) x)
20.0ms	(/ (pow t 2) x)
287.0ms	(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	837
1	1450	724
2	5001	715

prune400.0ms

Filtered

139 candidates to 96 candidates (30.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	133	13	146

Merged error: 2.0b

Counts

146 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
3.8b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.2b	(/ (pow t 2) x)
25.0b	(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

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))))
9.0ms	(/ (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)))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt 2.0) t)
74.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
20.0ms	(/ (pow t 2) x)
283.0ms	(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

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	321	653
1	1261	592
2	5002	586

prune313.0ms

Filtered

112 candidates to 76 candidates (32.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	111	14	125

Merged error: 2.0b

Counts

125 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
3.8b	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
10.2b	(/ (pow t 2) x)
25.0b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
45×	`sqrt-prod`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac` `unswap-sqr`
23×	`associate-r`
18×	`associate-l`
14×	`add-exp-log`
12×	`unpow-prod-down`
11×	`add-cbrt-cube`
10×	`pow1`
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`
2×	`*-commutative`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 133

Calls

4 calls:

15.0ms	(* (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)
5.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
68.0ms	(fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
26.0ms	(/ (pow t 2) x)
288.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	417	1052
1	1713	864
2	5001	845

prune356.0ms

Filtered

145 candidates to 90 candidates (37.9%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	4	7	11
Picked	0	1	1
Done	0	2	2
Total	142	17	159

Merged error: 2.0b

Counts

159 → 17

regimes578.0ms

Accuracy

78% (5.3b remaining)

Error of 9.0b against oracle of 3.7b and baseline of 27.6b

bsearch449.0ms

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

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	75
1	83	75
2	84	75
3	84	75

end0.0ms

sample2.2s

Algorithm

intervals

Results

549.0ms	10089×	body	80	nan
287.0ms	5160×	body	80	valid
228.0ms	1052×	body	640	valid
226.0ms	829×	body	1280	valid
164.0ms	605×	body	1280	nan
134.0ms	630×	body	640	nan
102.0ms	628×	body	320	valid
57.0ms	363×	body	320	nan
36.0ms	331×	body	160	valid
20.0ms	181×	body	160	nan