Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	337×	body	80	nan
11.0ms	39×	body	1280	valid
9.0ms	161×	body	80	valid
6.0ms	29×	body	640	valid
5.0ms	19×	body	1280	nan
4.0ms	21×	body	640	nan
2.0ms	15×	body	320	valid
2.0ms	14×	body	320	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify96.0ms

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: 46.0b

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))))
0.4b	(* (sqrt 2.0) t)
12.9b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite63.0ms

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:

18.0ms	(/ (* (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)
14.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

432.0ms	(/ (* (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)
224.0ms	(- (* (/ (+ 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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (51.0ms)

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

prune328.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	4	103

Merged error: 8.3b

Counts

103 → 4

localize18.0ms

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))))
6.2b	(/ (pow l 2) x)
8.1b	(/ (pow t 2) x)
28.4b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite20.0ms

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)
9.0ms	(/ (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)))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(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)
19.0ms	(/ (pow t 2) x)
275.0ms	(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

prune437.0ms

Filtered

139 candidates to 96 candidates (69.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	134	9	143

Merged error: 5.8b

Counts

143 → 9

localize17.0ms

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 (/ x l)) (* 4.0 (/ (pow t 2) x))))
8.1b	(/ (pow t 2) x)
28.4b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 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 (/ x l)) (* 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 (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sqrt 2.0) t)
69.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
264.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	322	653
1	1220	592
2	5001	586

prune336.0ms

Filtered

112 candidates to 77 candidates (68.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 5.8b

Counts

121 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
4.0b	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
8.1b	(/ (pow t 2) x)
28.4b	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

11.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
1.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 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 (/ x l)) (* 4.0 (/ (pow t 2) x)))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
70.0ms	(fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
273.0ms	(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ l (/ x l)) (* 4.0 (/ (pow t 2) x)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	372	843
1	1378	691
2	5001	641

prune333.0ms

Filtered

112 candidates to 75 candidates (67.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	111	11	122

Merged error: 5.8b

Counts

122 → 11

regimes326.0ms

Accuracy

76.3% (5.6b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 27.7b

bsearch591.0ms

Steps

Iters	Range		Point
9	8.035144973212608e+106	2.245460825297648e+113	4.237815991261577e+112
4	1.2124728414118423e-211	2.2847307266758587e-211	2.2297033326087545e-211
7	1.915898718087215e-234	4.464915074202446e-232	8.22209001535682e-233
8	-1.243875693689644e-199	-2.0983465895690414e-202	-1.2665252057061608e-201
7	-7.309844064450707e-163	-5.607849872840746e-165	-5.9781316899939775e-164
10	-1.1430041385930207e+102	-1.1718803704805511e+85	-2.5865283365572245e+92

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	123
1	106	123
2	107	123
3	107	123

end0.0ms

sample2.1s

Algorithm

intervals

Results

489.0ms	9926×	body	80	nan
270.0ms	5127×	body	80	valid
218.0ms	852×	body	1280	valid
212.0ms	1029×	body	640	valid
137.0ms	549×	body	1280	nan
123.0ms	607×	body	640	nan
93.0ms	637×	body	320	valid
48.0ms	319×	body	320	nan
35.0ms	355×	body	160	valid
17.0ms	175×	body	160	nan