Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	96×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	7×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

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: 15.7b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
3.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l` `difference-of-squares`
2×	`sqrt-prod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

1.0ms	(hypot 1.0 x)
3.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series97.0ms

Counts

3 → 9

Calls

3 calls:

1.0ms	(hypot 1.0 x)
5.0ms	(/ 1.0 (hypot 1.0 x))
91.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify125.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	166	365
1	479	340
2	1328	338
3	4568	338
4	5001	338

prune108.0ms

Filtered

59 candidates to 42 candidates (71.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	4	60

Merged error: 15.2b

Counts

60 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`associate-*r/`
36×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`frac-sub`
20×	`times-frac`
14×	`associate-/l*`
12×	`flip3--` `associate-/r*` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`unswap-sqr`
6×	`clear-num` `difference-of-squares`
4×	`pow1` `frac-2neg` `associate-l` `associate--l+` `un-div-inv` `distribute-lft-out--`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 114

Calls

4 calls:

11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
27.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
35.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify79.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	534	1148
1	2175	1096
2	5003	1094

prune290.0ms

Filtered

126 candidates to 87 candidates (69.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	127	3	130

Merged error: 15.2b

Counts

130 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))
0.1b	(* (sqrt (hypot 1.0 x)) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.1b	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
2.6b	(- (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x))) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

242×	`associate-*r/`
234×	`*-un-lft-identity`
229×	`add-sqr-sqrt`
177×	`associate-l`
96×	`associate-*l/`
88×	`frac-sub`
86×	`associate-r`
84×	`frac-times` `unswap-sqr`
76×	`distribute-lft-out`
62×	`sqrt-prod`
55×	`add-cube-cbrt`
54×	`associate-/r*`
46×	`flip3--` `flip3-+` `flip--` `flip-+`
38×	`distribute-lft-out--`
36×	`associate-/l*`
34×	`difference-of-squares`
32×	`times-frac`
20×	`add-exp-log` `add-cbrt-cube`
18×	`clear-num` `un-div-inv`
16×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`frac-2neg` `prod-exp` `cbrt-unprod`
8×	`unpow-prod-down` `associate-+l+`
7×	`pow-prod-down`
6×	`+-commutative` `add-log-exp` `sqr-pow`
5×	`*-commutative`
4×	`difference-cubes` `pow-unpow`
1×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 364

Calls

4 calls:

21.0ms	(* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))
24.0ms	(* (sqrt (hypot 1.0 x)) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
49.0ms	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
151.0ms	(- (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x))) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))
32.0ms	(* (sqrt (hypot 1.0 x)) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
38.0ms	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
94.0ms	(- (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x))) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))

simplify152.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	1916	9486
1	5001	9334

prune1.6s

Filtered

376 candidates to 220 candidates (58.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	372	4	376
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	373	6	379

Merged error: 14.8b

Counts

379 → 6

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
0.1b	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
0.3b	(* (+ (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))) (- (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))))
2.6b	(- (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

34594×	`associate-*r/`
32208×	`sqrt-div`
18404×	`frac-times`
16930×	`associate-*l/`
8144×	`flip3--` `flip--`
8096×	`frac-sub`
8008×	`frac-add`
6624×	`associate-/r*`
5611×	`flip3-+` `flip-+`
4894×	`*-un-lft-identity`
4416×	`associate-/l*`
3718×	`add-sqr-sqrt`
3706×	`sqrt-prod`
3350×	`add-cube-cbrt`
2208×	`clear-num` `un-div-inv`
1104×	`frac-2neg`
422×	`associate-l`
235×	`distribute-lft-out`
186×	`associate-r`
177×	`unswap-sqr`
74×	`distribute-lft-out--`
72×	`difference-of-squares`
68×	`times-frac`
24×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
11×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
6×	`add-log-exp`
5×	`*-commutative`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `div-inv`
1×	`diff-log`

Counts

4 → 8805

Calls

4 calls:

53.0ms	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
53.0ms	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
561.0ms	(* (+ (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))) (- (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))))
166.0ms	(- (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
44.0ms	(* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))
670.0ms	(* (+ (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))) (- (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x))))))))
323.0ms	(- (sqrt (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (sqrt (hypot 1.0 x)))) (sqrt (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (* 0.5 (/ 1.0 (sqrt (hypot 1.0 x)))))))

simplify10.7s

Algorithm

egg-herbie

Counts

8817 → 8817

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	8973	1144679

prune1.6m

Filtered

8817 candidates to 5621 candidates (63.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	8815	2	8817
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	8817	6	8823

Merged error: 14.8b

Counts

8823 → 6

regimes131.0ms

Accuracy

0% (0.3b remaining)

Error of 15.9b against oracle of 15.6b and baseline of 15.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	45	33

end0.0ms

sample809.0ms

Algorithm

intervals

Results

471.0ms	2898×	body	1280	valid
109.0ms	3947×	body	80	valid
81.0ms	640×	body	640	valid
28.0ms	329×	body	320	valid
10.0ms	186×	body	160	valid