Details

sample277.0ms

Algorithm

intervals

Results

201.0ms	172×	body	80	valid
9.0ms	27×	body	1280	nan
8.0ms	22×	body	1280	valid
8.0ms	109×	body	80	nan
7.0ms	26×	body	640	valid
6.0ms	22×	body	640	nan
4.0ms	22×	body	320	valid
3.0ms	16×	body	320	nan
2.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify356.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 43.0b

Counts

2 → 1

localize19.0ms

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)
12.4b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite68.0ms

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×	`sqrt-div`
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` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

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)
30.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
14.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* (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)
57.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
196.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune218.0ms

Filtered

92 candidates to 65 candidates (29.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 4.5b

Counts

93 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
1.0b	(pow (sqrt 2.0) 3)
8.2b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
8.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`div-exp`
13×	`prod-exp`
10×	`sqrt-prod`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`unpow-prod-down` `times-frac` `cube-prod` `associate-l` `associate-/l*`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `*-commutative` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
3.0ms	(pow (sqrt 2.0) 3)
10.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
6.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series29.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
0.0ms	(pow (sqrt 2.0) 3)
16.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
9.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify77.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	379	567
1	2149	506
2	5002	498

prune288.0ms

Filtered

116 candidates to 61 candidates (47.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	112	10	122

Merged error: 4.5b

Counts

122 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
1.0b	(pow (sqrt 2.0) 3)
8.2b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
8.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`div-exp`
13×	`prod-exp`
10×	`sqrt-prod`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`unpow-prod-down` `times-frac` `cube-prod` `associate-l` `associate-/l*`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `*-commutative` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
3.0ms	(pow (sqrt 2.0) 3)
7.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
6.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series31.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
0.0ms	(pow (sqrt 2.0) 3)
16.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
11.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify70.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	355	550
1	2003	487
2	5001	479

prune338.0ms

Filtered

116 candidates to 61 candidates (47.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	114	12	126

Merged error: 4.5b

Counts

126 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
8.2b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
8.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
14×	`div-exp` `add-cbrt-cube`
12×	`prod-exp`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow-to-exp` `pow-exp`
6×	`cbrt-prod` `times-frac` `associate-/l*`
4×	`pow1` `cbrt-undiv` `add-log-exp`
2×	`frac-2neg` `pow1/3` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
7.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
8.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series26.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
16.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
9.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	245	440
1	1025	387
2	5001	383

prune255.0ms

Filtered

82 candidates to 52 candidates (36.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	81	13	94

Merged error: 4.5b

Counts

94 → 13

regimes831.0ms

Accuracy

77.8% (5.3b remaining)

Error of 9.8b against oracle of 4.5b and baseline of 28.4b

bsearch477.0ms

Steps

Iters	Range		Point
10	-2.3377513339728866e-308	3.6655400293112513e-298	-3.212931526919e-310
7	-2.713795471243273e-241	-7.920380319605328e-243	-5.360578384546504e-242
9	-2.457263417881211e-205	-5.211746218194639e-212	-5.492869455238719e-207
10	-4.309370604141362e-135	-1.440605428335766e-149	-1.4635615870780773e-149
7	-2.416813801566695e+24	-6.766122571495881e+22	-4.1548218607575645e+23

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	114
1	68	114

end0.0ms

sample2.4s

Algorithm

intervals

Results

392.0ms	5521×	body	80	valid
296.0ms	886×	body	1280	nan
261.0ms	3759×	body	80	nan
233.0ms	873×	body	640	nan
233.0ms	688×	body	1280	valid
231.0ms	867×	body	640	valid
114.0ms	560×	body	320	valid
97.0ms	492×	body	320	nan
49.0ms	364×	body	160	valid
34.0ms	253×	body	160	nan

Details

sample277.0ms

simplify356.0ms

prune5.0ms

localize19.0ms

rewrite68.0ms

series348.0ms

simplify61.0ms

prune218.0ms

localize24.0ms

rewrite26.0ms

series29.0ms

simplify77.0ms

prune288.0ms

localize29.0ms

rewrite24.0ms

series31.0ms

simplify70.0ms

prune338.0ms

localize32.0ms

rewrite20.0ms

series26.0ms

simplify34.0ms

prune255.0ms

regimes831.0ms

bsearch477.0ms

simplify3.0ms

end0.0ms

sample2.4s

Profiling