Details

sample117.0ms

Algorithm

intervals

Results

26.0ms	343×	body	80	nan
14.0ms	31×	body	640	valid
13.0ms	166×	body	80	valid
10.0ms	26×	body	1280	valid
9.0ms	23×	body	1280	nan
7.0ms	23×	body	640	nan
4.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	6×	body	320	nan
1.0ms	5×	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

prune6.0ms

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: 42.6b

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))))
0.4b	(* (sqrt 2.0) t)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite60.0ms

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))))
5.0ms	(* (sqrt 2.0) t)
20.0ms	(- (* (/ (+ 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)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* (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)
61.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
207.0ms	(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 (47.0ms)

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

prune227.0ms

Filtered

92 candidates to 65 candidates (29.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 5.1b

Counts

93 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

6.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.3b	(/ (pow l 2) x)
7.6b	(/ (pow t 2) x)
26.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite32.0ms

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms	(/ (pow l 2) x)
3.0ms	(/ (pow t 2) x)
26.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

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

prune372.0ms

Filtered

142 candidates to 97 candidates (31.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	140	7	147

Merged error: 2.6b

Counts

147 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
6.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
7.6b	(/ (pow t 2) x)
26.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite28.0ms

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))))
9.0ms	(+ (* 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)))))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
21.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
3.0ms	(/ (pow t 2) x)
29.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	463	1321
1	2029	1213
2	5003	1210

prune256.0ms

Filtered

104 candidates to 75 candidates (27.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Merged error: 2.6b

Counts

111 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

5.8b	(exp (log (sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))))
6.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
7.6b	(/ (pow t 2) x)
26.0b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

10.0ms	(exp (log (sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))))
11.0ms	(+ (* 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)))))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (log (sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))))
18.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
3.0ms	(/ (pow t 2) x)
28.0ms	(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

117 → 117

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	491	1776
1	1992	1672
2	5002	1627

prune293.0ms

Filtered

117 candidates to 84 candidates (28.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	115	10	125

Merged error: 2.6b

Counts

125 → 10

regimes679.0ms

Accuracy

75.8% (5.7b remaining)

Error of 9.6b against oracle of 3.9b and baseline of 27.6b

bsearch277.0ms

Steps

Iters	Range		Point
3	1.6058776025918372e+63	2.01951895708704e+63	1.991189687760504e+63
9	1.785946959370076e-166	1.2354839038895813e-158	1.3317334991218154e-160
9	3.8930897825126873e-258	4.4458512927026374e-253	4.547225514729844e-255
8	-1.0831081380062595e+86	-1.658459307074215e+83	-8.81655015220474e+84

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	102
1	75	102
2	78	102
3	78	102

end0.0ms

sample3.1s

Algorithm

intervals

Results

722.0ms	10210×	body	80	nan
366.0ms	5090×	body	80	valid
317.0ms	899×	body	1280	valid
293.0ms	1037×	body	640	valid
215.0ms	607×	body	1280	nan
183.0ms	653×	body	640	nan
124.0ms	601×	body	320	valid
72.0ms	353×	body	320	nan
51.0ms	373×	body	160	valid
29.0ms	203×	body	160	nan

Details

sample117.0ms

simplify84.0ms

prune6.0ms

localize19.0ms

rewrite60.0ms

series366.0ms

simplify60.0ms

prune227.0ms

localize17.0ms

rewrite32.0ms

series48.0ms

simplify61.0ms

prune372.0ms

localize24.0ms

rewrite28.0ms

series66.0ms

simplify60.0ms

prune256.0ms

localize26.0ms

rewrite36.0ms

series81.0ms

simplify61.0ms

prune293.0ms

regimes679.0ms

bsearch277.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling