Details

sample49.0ms

Algorithm

intervals

Results

11.0ms	25×	body	1280	valid
10.0ms	191×	body	80	valid
6.0ms	20×	body	2560	valid
5.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	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

prune3.0ms

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: 14.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.9b	(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:

7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.0ms	(+ (* (* 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)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify146.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4232	757
3	5001	757

prune207.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	76	15	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	15	92

Merged error: 14.5b

Counts

92 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify83.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	231	541
1	855	487
2	2820	483
3	5001	482

prune180.0ms

Filtered

54 candidates to 67 candidates (-24.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	67	15	82

Merged error: 14.5b

Counts

82 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 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))))))
12.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite33.0ms

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:

7.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
15.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series37.0ms

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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	367	1195
1	1649	1076
2	5001	1014

prune240.0ms

Filtered

78 candidates to 134 candidates (-71.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	134	15	149

Merged error: 14.5b

Counts

149 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
2.9b	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
12.9b	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`unpow-prod-down` `associate-r`
6×	`add-cbrt-cube`
5×	`pow1`
3×	`pow-unpow` `associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `sum-log` `flip-+`
1×	`pow-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
9.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
3.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
5.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

series49.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
9.0ms	(* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2))
14.0ms	(+ 1.0 (* x (pow (+ (* (* 4.0 p) p) (* x x)) -1/2)))
20.0ms	(pow (+ (* (* 4.0 p) p) (* x x)) -1/2)

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	321	587
1	1361	545
2	5001	539

prune130.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	77	14	91

Merged error: 14.5b

Counts

91 → 14

regimes260.0ms

Accuracy

0% (0.5b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	11
1	24	11

end0.0ms

sample1.3s

Algorithm

intervals

Results

328.0ms	6029×	body	80	valid
269.0ms	818×	body	2560	valid
165.0ms	611×	body	1280	valid
133.0ms	8000×	pre	80	true
61.0ms	297×	body	640	valid
25.0ms	163×	body	320	valid
8.0ms	82×	body	160	valid

Details

sample49.0ms

simplify9.0ms

prune3.0ms

localize12.0ms

rewrite29.0ms

series37.0ms

simplify146.0ms

prune207.0ms

localize15.0ms

rewrite35.0ms

series39.0ms

simplify83.0ms

prune180.0ms

localize12.0ms

rewrite33.0ms

series37.0ms

simplify47.0ms

prune240.0ms

localize16.0ms

rewrite23.0ms

series49.0ms

simplify44.0ms

prune130.0ms

regimes260.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

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