Details

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 74.54834%

Results

11.0ms	215×	body	80	valid
6.0ms	21×	body	2560	valid
4.0ms	256×	pre	80	true
2.0ms	9×	body	1280	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	4×	body	160	valid

simplify8.0ms

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: 8.5b

Counts

2 → 1

localize10.0ms

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))))
0.9b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

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

series32.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 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)))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify143.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (25.0ms)

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

prune182.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

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: 8.3b

Counts

92 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
5.1b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3-+` `sqrt-div` `cube-prod` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `sum-cubes` `div-inv`

Counts

4 → 98

Calls

4 calls:

35.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	352	1043
1	1550	965
2	5001	964

prune344.0ms

Filtered

81 candidates to 110 candidates (-35.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 8.3b

Counts

118 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

6.0ms	(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)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify82.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune672.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 8.3b

Counts

80 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
17.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (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))
8.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	387	817
1	1913	734
2	5002	700

prune153.0ms

Filtered

69 candidates to 98 candidates (-42.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	98	9	107

Merged error: 8.3b

Counts

107 → 9

regimes202.0ms

Accuracy

0% (1.4b remaining)

Error of 14.2b against oracle of 12.8b and baseline of 14.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	17
1	21	17

end0.0ms

sample2.8s

Algorithm

intervals

sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 74.54834%

Results

322.0ms	6039×	body	80	valid
275.0ms	840×	body	2560	valid
152.0ms	588×	body	1280	valid
149.0ms	8000×	pre	80	true
66.0ms	309×	body	640	valid
23.0ms	150×	body	320	valid
8.0ms	74×	body	160	valid

Details

sample1.5s

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite32.0ms

series32.0ms

simplify143.0ms

prune182.0ms

localize21.0ms

rewrite54.0ms

series38.0ms

simplify51.0ms

prune344.0ms

localize32.0ms

rewrite22.0ms

series29.0ms

simplify82.0ms

prune672.0ms

localize12.0ms

rewrite28.0ms

series35.0ms

simplify51.0ms

prune153.0ms

regimes202.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling