Details

sample107.0ms

Algorithm

intervals

Results

22.0ms	310×	body	80	nan
16.0ms	28×	body	1280	valid
11.0ms	159×	body	80	valid
10.0ms	36×	body	640	valid
8.0ms	23×	body	1280	nan
5.0ms	18×	body	640	nan
4.0ms	22×	body	320	valid
3.0ms	14×	body	320	nan
2.0ms	13×	body	160	nan
2.0ms	11×	body	160	valid

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (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: 45.2b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (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)
15.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(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×	`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:

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)
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)))

series1.9s

Counts

4 → 12

Calls

4 calls:

420.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
42.0ms	(* (sqrt 2.0) t)
208.0ms	(- (* (/ (+ 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

92 → 92

Iterations

Useful iterations: 1 (12.0ms)

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

prune290.0ms

Filtered

92 candidates to 68 candidates (73.9%)

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: 6.5b

Counts

93 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.2b	(/ (pow l 2) x)
10.3b	(/ (pow t 2) x)
27.9b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite31.0ms

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:

9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
161.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	526	1093
1	2235	984
2	5001	978

prune416.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Merged error: 3.5b

Counts

148 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* l (/ l x)))
2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.3b	(/ (pow t 2) x)
27.9b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite29.0ms

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:

5.0ms	(+ (pow t 2) (* l (/ l x)))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (pow t 2) (* l (/ l x)))
64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	456	925
1	1936	858
2	5001	855

prune304.0ms

Filtered

104 candidates to 75 candidates (72.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	103	13	116

Merged error: 3.5b

Counts

116 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

10.3b	(/ (pow t 2) x)
27.9b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))
28.1b	(sqrt (+ (pow t 2) (* l (/ l x))))
28.1b	(sqrt (+ (pow t 2) (* l (/ l x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
9×	`add-exp-log` `flip3-+` `sqrt-prod` `flip-+`
8×	`frac-add` `associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`frac-times` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
2×	`associate-*l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

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

series316.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (pow t 2) x)
157.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))
68.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))
70.0ms	(sqrt (+ (pow t 2) (* l (/ l x))))

simplify61.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	511	1344
1	1766	1286
2	5002	1281

prune345.0ms

Filtered

114 candidates to 83 candidates (72.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	115	12	127

Merged error: 3.5b

Counts

127 → 12

regimes430.0ms

Accuracy

73.6% (6.2b remaining)

Error of 9.8b against oracle of 3.6b and baseline of 27.2b

bsearch858.0ms

Steps

Iters	Range		Point
10	4.303922473367365e+108	1.931316243244326e+118	8.28827763547494e+114
7	5.834548822037511e-190	5.310846843265014e-188	3.179593151054512e-188
8	2.0531948601770492e-296	1.9147608801785507e-293	1.8906625567539152e-293
9	1.602615327513597e-304	1.997368604160002e-299	1.617668931297377e-304
10	-1.3111885523472323e-180	-7.354709209583203e-196	-1.492381997315763e-189
9	-4.927324273936486e+121	-1.6988174615908472e+112	-1.5746361320052905e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	132
1	89	132

end0.0ms

sample2.8s

Algorithm

intervals

Results

704.0ms	9963×	body	80	nan
376.0ms	5153×	body	80	valid
299.0ms	860×	body	1280	valid
260.0ms	937×	body	640	valid
202.0ms	591×	body	1280	nan
158.0ms	592×	body	640	nan
145.0ms	705×	body	320	valid
72.0ms	360×	body	320	nan
48.0ms	345×	body	160	valid
25.0ms	188×	body	160	nan