Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
2.0ms	12×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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: 11.6b

Counts

2 → 1

localize11.0ms

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)))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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))
11.0ms	(/ 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)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify160.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune276.0ms

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: 11.3b

Counts

92 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite42.0ms

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:

13.0ms	(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)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
174.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify109.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (40.0ms)

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

prune258.0ms

Filtered

72 candidates to 57 candidates (79.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	73	11	84

Merged error: 8.1b

Counts

84 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.2b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
7×	`sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unpow2` `sqr-pow`
3×	`flip3-+` `div-exp` `associate-/r*` `flip-+` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 97

Calls

4 calls:

12.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	325	1030
1	1289	956
2	5001	954

prune394.0ms

Filtered

109 candidates to 81 candidates (74.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	109	11	120

Merged error: 8.1b

Counts

120 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow E (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`pow1` `log-prod`
6×	`add-exp-log` `add-log-exp`
4×	`unpow-prod-up` `log-div` `pow-unpow` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-down` `sqrt-prod` `distribute-lft-out`
2×	`sqrt-div` `pow-exp` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

13.0ms	(pow E (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ 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)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(pow E (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
185.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	292	860
1	847	782
2	2726	767
3	5001	755

prune194.0ms

Filtered

79 candidates to 57 candidates (72.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	6	3	9
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 5.1b

Counts

90 → 7

regimes197.0ms

Accuracy

84.9% (1.0b remaining)

Error of 7.8b against oracle of 6.8b and baseline of 13.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

335.0ms	6024×	body	80	valid
278.0ms	819×	body	2560	valid
172.0ms	609×	body	1280	valid
158.0ms	8000×	pre	80	true
71.0ms	311×	body	640	valid
24.0ms	152×	body	320	valid
9.0ms	85×	body	160	valid