Details

analyze751.0ms

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

sample40.0ms

Algorithm

intervals

Results

10.0ms	196×	body	80	valid
7.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
3.0ms	5×	body	320	valid
2.0ms	9×	body	640	valid
0.0ms	5×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune6.0ms

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: 12.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

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))))
11.0ms	(+ 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:

8.0ms	(+ (* (* 4.0 p) p) (* x x))
9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4982	1385
1	4982	1385

prune202.0ms

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: 12.0b

Counts

92 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
2.8b	(log (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
16.6b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
26.0ms	(log (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify83.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5315	1560

prune208.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 8.3b

Counts

106 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
16.6b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
16.6b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
16.6b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(log (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
9.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5044	970

prune293.0ms

Filtered

59 candidates to 72 candidates (-22.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	71	10	81

Merged error: 8.3b

Counts

81 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
4.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
16.6b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
14.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
5.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1 (sqrt (+ (* 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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5233	1899

prune184.0ms

Filtered

83 candidates to 134 candidates (-61.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	132	12	144

Merged error: 8.3b

Counts

144 → 12

regimes160.0ms

Accuracy

0% (3.8b remaining)

Error of 13.3b against oracle of 9.5b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	54
1	24	54

end0.0ms

analyze731.0ms

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

sample1.1s

Algorithm

intervals

Results

307.0ms	6092×	body	80	valid
244.0ms	783×	body	2560	valid
146.0ms	587×	body	1280	valid
138.0ms	8000×	pre	80	true
63.0ms	314×	body	640	valid
21.0ms	145×	body	320	valid
10.0ms	79×	body	160	valid

Details

analyze751.0ms

sample40.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite29.0ms

series36.0ms

simplify48.0ms

prune202.0ms

localize14.0ms

rewrite39.0ms

series54.0ms

simplify83.0ms

prune208.0ms

localize20.0ms

rewrite29.0ms

series48.0ms

simplify60.0ms

prune293.0ms

localize13.0ms

rewrite36.0ms

series38.0ms

simplify74.0ms

prune184.0ms

regimes160.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze731.0ms

sample1.1s

Profiling