Details

analyze781.0ms

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

sample43.0ms

Algorithm

intervals

Results

12.0ms	184×	body	80	valid
9.0ms	30×	body	2560	valid
5.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	13×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	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

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: 14.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))))
13.8b	(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`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(/ 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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5576	1479

prune208.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 14.5b

Counts

94 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
0.5b	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 0.5))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
2.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 0.5))))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))
30.0ms	(log (exp (sqrt (* (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))) 0.5))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4901	1562
1	4901	1562

prune236.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	94	12	106

Merged error: 14.5b

Counts

106 → 12

localize12.0ms

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)))))
3.5b	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite29.0ms

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:

4.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))))
14.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 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))))))
9.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4929	1384
1	4929	1384

prune200.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	101	11	112

Merged error: 14.5b

Counts

112 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.1b	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) 0.5))))
3.5b	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
13.8b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

14.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
2.0ms	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) 0.5))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
30.0ms	(log (exp (sqrt (* (+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) 0.5))))
14.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4965	1467
1	4965	1467

prune182.0ms

Filtered

74 candidates to 103 candidates (-39.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 14.5b

Counts

114 → 12

regimes185.0ms

Accuracy

0% (0.6b remaining)

Error of 13.4b against oracle of 12.9b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	21
1	24	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

315.0ms	6042×	body	80	valid
256.0ms	815×	body	2560	valid
155.0ms	610×	body	1280	valid
143.0ms	8000×	pre	80	true
59.0ms	296×	body	640	valid
23.0ms	157×	body	320	valid
8.0ms	80×	body	160	valid

Details

analyze781.0ms

sample43.0ms

simplify3.0ms

prune7.0ms

localize11.0ms

rewrite39.0ms

series63.0ms

simplify69.0ms

prune208.0ms

localize14.0ms

rewrite32.0ms

series58.0ms

simplify66.0ms

prune236.0ms

localize12.0ms

rewrite29.0ms

series60.0ms

simplify44.0ms

prune200.0ms

localize16.0ms

rewrite28.0ms

series61.0ms

simplify60.0ms

prune182.0ms

regimes185.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling