Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	196×	body	80	valid
6.0ms	21×	body	2560	valid
6.0ms	11×	body	640	valid
5.0ms	256×	pre	80	true
5.0ms	20×	body	1280	valid
1.0ms	5×	body	160	valid
0.0ms	3×	body	320	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

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: 12.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify152.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4232	757
3	5001	757

prune249.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	12	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 12.5b

Counts

92 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.2b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
18.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `log-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`log-div` `exp-prod` `flip3-+` `exp-sum` `add-cbrt-cube` `flip-+`
3×	`sqrt-prod` `distribute-lft-out`
2×	`exp-diff` `sqrt-div` `log-pow`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `rem-exp-log`

Counts

4 → 60

Calls

4 calls:

17.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
180.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify121.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	230	707
1	588	645
2	1449	625
3	3630	619
4	5001	619

prune207.0ms

Filtered

72 candidates to 54 candidates (75.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 8.6b

Counts

84 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`pow1` `add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`log-pow`
4×	`log-prod` `exp-prod` `sqrt-div`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`associate-/r/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `exp-sum` `clear-num` `sum-log` `div-inv`

Counts

4 → 85

Calls

4 calls:

8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	269	900
1	805	835
2	2267	823
3	5003	822

prune265.0ms

Filtered

97 candidates to 73 candidates (75.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 8.6b

Counts

105 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.9b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
18.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `prod-exp` `flip-+`
3×	`sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
13.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	390	903
1	1699	818
2	5001	784

prune212.0ms

Filtered

100 candidates to 72 candidates (72.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	101	8	109

Merged error: 8.6b

Counts

109 → 8

regimes110.0ms

Accuracy

0% (3.9b remaining)

Error of 13.5b against oracle of 9.6b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

305.0ms	6052×	body	80	valid
240.0ms	782×	body	2560	valid
153.0ms	586×	body	1280	valid
140.0ms	8000×	pre	80	true
65.0ms	329×	body	640	valid
26.0ms	165×	body	320	valid
8.0ms	86×	body	160	valid

Details

sample46.0ms

simplify11.0ms

prune3.0ms

localize12.0ms

rewrite31.0ms

series227.0ms

simplify152.0ms

prune249.0ms

localize15.0ms

rewrite46.0ms

series388.0ms

simplify121.0ms

prune207.0ms

localize19.0ms

rewrite39.0ms

series267.0ms

simplify75.0ms

prune265.0ms

localize13.0ms

rewrite31.0ms

series463.0ms

simplify51.0ms

prune212.0ms

regimes110.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling