Details

analyze764.0ms

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	193×	body	80	valid
8.0ms	27×	body	2560	valid
5.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	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: 13.1b

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))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite36.0ms

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))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(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 (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify36.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4994	1385
1	4994	1385

prune195.0ms

Filtered

71 candidates to 91 candidates (-28.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 12.9b

Counts

92 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(* x (/ x (+ (* 4.0 (* p p)) (* x x))))
2.9b	(/ x (+ (* 4.0 (* p p)) (* x x)))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.5b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

12.0ms	(* x (/ x (+ (* 4.0 (* p p)) (* x x))))
7.0ms	(/ x (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* x (/ x (+ (* 4.0 (* p p)) (* x x))))
8.0ms	(/ x (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4955	1402
1	4955	1402

prune308.0ms

Filtered

81 candidates to 105 candidates (-29.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 12.9b

Counts

113 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))
6.1b	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* 4.0 (* p p)) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
16.2b	(cbrt (+ (* 4.0 (* p p)) (* x x)))
16.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `cbrt-div`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1/3`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 65

Calls

4 calls:

3.0ms	(/ x (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))
34.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* 4.0 (* p p)) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ x (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))
61.0ms	(+ 1.0 (/ (/ x (fabs (cbrt (+ (* 4.0 (* p p)) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
22.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
22.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5184	1552

prune241.0ms

Filtered

66 candidates to 77 candidates (-16.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 12.9b

Counts

85 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))) (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))
6.1b	(+ 1.0 (/ x (* (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))) (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))))
16.2b	(cbrt (+ (* 4.0 (* p p)) (* x x)))
16.2b	(cbrt (+ (* 4.0 (* p p)) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`cbrt-prod` `add-cube-cbrt`
9×	`associate-l`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-r` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*l/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 66

Calls

4 calls:

11.0ms	(* (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))) (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))
7.0ms	(+ 1.0 (/ x (* (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))) (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))) (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))
61.0ms	(+ 1.0 (/ x (* (sqrt (cbrt (+ (* 4.0 (* p p)) (* x x)))) (fabs (cbrt (+ (* 4.0 (* p p)) (* x x)))))))
26.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
23.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4940	1793
1	4940	1793

prune252.0ms

Filtered

65 candidates to 78 candidates (-20.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	74	13	87

Merged error: 12.9b

Counts

87 → 13

regimes219.0ms

Accuracy

77% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.9b

bsearch16.0ms

Steps

Iters	Range		Point
4	-1.5972327553387234e-149	-9.52278731822032e-150	-1.2830507578319113e-149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	117
1	68	117

end0.0ms

sample1.1s

Algorithm

intervals

Results

323.0ms	6079×	body	80	valid
253.0ms	788×	body	2560	valid
152.0ms	583×	body	1280	valid
143.0ms	8000×	pre	80	true
61.0ms	303×	body	640	valid
28.0ms	174×	body	320	valid
9.0ms	73×	body	160	valid

Details

analyze764.0ms

sample40.0ms

simplify3.0ms

prune6.0ms

localize12.0ms

rewrite36.0ms

series35.0ms

simplify36.0ms

prune195.0ms

localize23.0ms

rewrite35.0ms

series33.0ms

simplify65.0ms

prune308.0ms

localize20.0ms

rewrite49.0ms

series124.0ms

simplify44.0ms

prune241.0ms

localize21.0ms

rewrite32.0ms

series148.0ms

simplify59.0ms

prune252.0ms

regimes219.0ms

bsearch16.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling