Details

analyze813.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample41.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
8.0ms	23×	body	2560	valid
7.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	8×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.2b

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))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

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:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
17.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4994	1385
1	4994	1385

prune213.0ms

Filtered

71 candidates to 91 candidates (-28.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	80	11	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 11.9b

Counts

92 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 3)
0.0b	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 3))
0.5b	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
15.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod`
6×	`pow1` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`cube-div` `flip3-+` `flip-+`
3×	`pow-unpow` `sqrt-prod`
2×	`cube-mult` `cbrt-div` `sqrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

16.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 3)
15.0ms	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 3))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 3)
12.0ms	(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 3))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4945	1533
1	4945	1533

prune198.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	89	13	102

Merged error: 11.9b

Counts

102 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 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))))))
15.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(+ (* 4.0 (* p p)) (* x x))
17.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 4.0 (* p p)) (* x x))
9.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
12.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4979	1290
1	4979	1290

prune197.0ms

Filtered

68 candidates to 98 candidates (-44.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Merged error: 11.9b

Counts

111 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0b	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
15.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.7b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

39×	`sqrt-prod`
27×	`associate-r`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
11×	`pow1`
10×	`sqrt-div`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`+-commutative` `frac-times` `associate-l` `associate-l/` `sum-log` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

29.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
3.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
13.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
10.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4966	1616
1	4966	1616

prune205.0ms

Filtered

72 candidates to 98 candidates (-36.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 11.9b

Counts

109 → 12

regimes165.0ms

Accuracy

0% (1.2b remaining)

Error of 14.0b against oracle of 12.7b and baseline of 14.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	34
1	25	34

end0.0ms

sample1.2s

Algorithm

intervals

Results

328.0ms	6067×	body	80	valid
251.0ms	766×	body	2560	valid
161.0ms	605×	body	1280	valid
145.0ms	8000×	pre	80	true
72.0ms	337×	body	640	valid
26.0ms	158×	body	320	valid
7.0ms	67×	body	160	valid

Details

analyze813.0ms

sample41.0ms

simplify4.0ms

prune7.0ms

localize12.0ms

rewrite39.0ms

series36.0ms

simplify37.0ms

prune213.0ms

localize15.0ms

rewrite56.0ms

series61.0ms

simplify52.0ms

prune198.0ms

localize13.0ms

rewrite36.0ms

series35.0ms

simplify51.0ms

prune197.0ms

localize17.0ms

rewrite48.0ms

series41.0ms

simplify53.0ms

prune205.0ms

regimes165.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling