Details

sample121.0ms

Algorithm

intervals

Results

30.0ms	36×	body	640	valid
20.0ms	292×	body	80	nan
11.0ms	160×	body	80	valid
10.0ms	29×	body	1280	valid
5.0ms	15×	body	1280	nan
4.0ms	17×	body	640	nan
4.0ms	19×	body	320	valid
3.0ms	17×	body	320	nan
2.0ms	12×	body	160	valid
0.0ms	2×	body	160	nan

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

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: 42.4b

Counts

2 → 1

localize25.0ms

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))
19.9b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite50.0ms

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)
12.0ms	(- (* (/ (+ 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)))

series2.2s

Counts

4 → 12

Calls

4 calls:

502.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
54.0ms	(* (sqrt 2.0) t)
250.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (48.0ms)

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

prune405.0ms

Filtered

92 candidates to 65 candidates (29.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	5	93

Merged error: 6.6b

Counts

93 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.2b	(/ (pow t 2) x)
8.5b	(/ (pow l 2) x)
26.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite29.0ms

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×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow t 2) x)
5.0ms	(/ (pow l 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
22.0ms	(/ (pow t 2) x)
28.0ms	(/ (pow l 2) x)
203.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978

prune1.5s

Filtered

142 candidates to 97 candidates (31.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	137	10	147

Merged error: 3.5b

Counts

147 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
7.2b	(/ (pow t 2) x)
26.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
99.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
22.0ms	(/ (pow t 2) x)
229.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	463	1308
1	1965	1213
2	5001	1210

prune873.0ms

Filtered

104 candidates to 75 candidates (27.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	104	10	114

Merged error: 3.5b

Counts

114 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

7.2b	(/ (pow t 2) x)
7.2b	(/ (pow t 2) x)
26.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))
26.3b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`sqrt-div` `associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`pow1` `div-exp` `associate-/r*` `sqrt-prod`
4×	`flip3-+` `frac-add` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

5.0ms	(/ (pow t 2) x)
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (pow t 2) x)
22.0ms	(/ (pow t 2) x)
228.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))
250.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	389	1444
1	1639	1356
2	5001	1350

prune1.1s

Filtered

144 candidates to 100 candidates (30.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	143	11	154

Merged error: 3.5b

Counts

154 → 11

regimes831.0ms

Accuracy

76.1% (5.7b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 27.7b

bsearch1.1s

Steps

Iters	Range		Point
10	7.558095329194679e+127	1.7475322207653267e+139	8.727670702867812e+130
9	1.3008927428624606e-216	3.371840907771101e-208	7.5927611501542e-210
11	1.4984913097511935e-287	2.797634192908259e-265	9.383349838959862e-269
10	-1.206899095635087e-240	-2.1727958469808713e-252	-2.114491288260618e-243
6	-1.50860837091955e-195	-1.62294574615281e-196	-3.656284367858482e-196
7	-1.0087625308462326e+68	-3.20233221123102e+66	-9.773561532294276e+67

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	141
1	95	141

end0.0ms

sample2.8s

Algorithm

intervals

Results

650.0ms	10115×	body	80	nan
340.0ms	5059×	body	80	valid
281.0ms	878×	body	1280	valid
261.0ms	1033×	body	640	valid
191.0ms	596×	body	1280	nan
168.0ms	652×	body	640	nan
128.0ms	663×	body	320	valid
68.0ms	364×	body	320	nan
48.0ms	367×	body	160	valid
23.0ms	187×	body	160	nan

Details

sample121.0ms

simplify84.0ms

prune7.0ms

localize25.0ms

rewrite50.0ms

series2.2s

simplify60.0ms

prune405.0ms

localize20.0ms

rewrite29.0ms

series331.0ms

simplify62.0ms

prune1.5s

localize25.0ms

rewrite27.0ms

series418.0ms

simplify61.0ms

prune873.0ms

localize25.0ms

rewrite31.0ms

series523.0ms

simplify57.0ms

prune1.1s

regimes831.0ms

bsearch1.1s

simplify4.0ms

end0.0ms

sample2.8s

Profiling