Details

analyze1.5s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 36.890989%

Guaranteed chance to sample good point: 48.262548%

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	53×	body	80	invalid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	50	6
2	159	6
3	351	6
4	609	6
5	733	6
6	1068	6
7	1342	6
8	1506	6
9	1553	6
10	1553	6

prune4.0ms

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: 6.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.7b	(* (* y 4.0) (- (* z z) t))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `sub-neg`
4×	`distribute-rgt-in` `add-cube-cbrt` `-un-lft-identity` `distribute-lft-in` `associate-r*` `associate--r+`
3×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 54

Calls

3 calls:

4.0ms	(- (* z z) t)
4.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
12.0ms	(* (* y 4.0) (- (* z z) t))

series37.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(- (* z z) t)
21.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
13.0ms	(* (* y 4.0) (- (* z z) t))

simplify43.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	292	385
1	1348	342
2	5001	337

prune86.0ms

Filtered

41 candidates to 63 candidates (-53.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 1.7b

Counts

64 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (* (* y 4.0) (- (* z z) t)))
5.7b	(* (* y 4.0) (- (* z z) t))
5.7b	(* (* y 4.0) (- (* z z) t))
5.7b	(* (* y 4.0) (- (* z z) t))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
10×	`add-sqr-sqrt`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`associate-*r/`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
4×	`flip3--` `flip--` `add-log-exp`
3×	`associate-l` `*-commutative` `difference-of-squares`
2×	`cbrt-div`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 86

Calls

4 calls:

6.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
8.0ms	(* (* y 4.0) (- (* z z) t))
8.0ms	(* (* y 4.0) (- (* z z) t))
8.0ms	(* (* y 4.0) (- (* z z) t))

series77.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
15.0ms	(* (* y 4.0) (- (* z z) t))
13.0ms	(* (* y 4.0) (- (* z z) t))
13.0ms	(* (* y 4.0) (- (* z z) t))

simplify39.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	289	620
1	1143	522
2	5001	517

prune152.0ms

Filtered

61 candidates to 98 candidates (-60.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Merged error: 1.7b

Counts

106 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
1.0b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
5.7b	(* (* y 4.0) (- (* z z) t))
5.7b	(* (* y 4.0) (- (* z z) t))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sqrt-div` `associate-*r/` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

3.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
3.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
8.0ms	(* (* y 4.0) (- (* z z) t))
8.0ms	(* (* y 4.0) (- (* z z) t))

series100.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
36.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
15.0ms	(* (* y 4.0) (- (* z z) t))
13.0ms	(* (* y 4.0) (- (* z z) t))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	270	654
1	1170	602
2	5002	598

prune130.0ms

Filtered

62 candidates to 92 candidates (-48.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	92	8	100

Merged error: 1.7b

Counts

100 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
5.7b	(sqrt (- (* z z) t))
5.7b	(sqrt (- (* z z) t))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-r`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
15.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
4.0ms	(sqrt (- (* z z) t))
4.0ms	(sqrt (- (* z z) t))

series42.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
13.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
6.0ms	(sqrt (- (* z z) t))
9.0ms	(sqrt (- (* z z) t))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	370	769
1	1754	653
2	5002	647

prune88.0ms

Filtered

69 candidates to 101 candidates (-46.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	101	8	109

Merged error: 1.7b

Counts

109 → 8

regimes979.0ms

Accuracy

81.6% (0.6b remaining)

Error of 3.3b against oracle of 2.7b and baseline of 5.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

analyze1.5s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 36.890989%

Guaranteed chance to sample good point: 48.262548%

sample636.0ms

Algorithm

intervals

Results

306.0ms	8000×	body	80	valid
76.0ms	2052×	body	80	invalid

Details

analyze1.5s

sample23.0ms

simplify75.0ms

prune4.0ms

localize9.0ms

rewrite21.0ms

series37.0ms

simplify43.0ms

prune86.0ms

localize13.0ms

rewrite33.0ms

series77.0ms

simplify39.0ms

prune152.0ms

localize11.0ms

rewrite25.0ms

series100.0ms

simplify45.0ms

prune130.0ms

localize11.0ms

rewrite35.0ms

series42.0ms

simplify53.0ms

prune88.0ms

regimes979.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze1.5s

sample636.0ms

Profiling