Details

sample357.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 69.726563%

Guaranteed chance to sample good point: 93.175403%

Results

20.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	15
1	161	15
2	459	15
3	1323	15
4	2992	15
5	5001	15

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: 0.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(* (* b b) (- 1.0 (* 3.0 a)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms	(* (* a a) (+ 1.0 a))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series59.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
5.0ms	(* (* a a) (+ 1.0 a))
9.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	547	721
1	2714	641
2	5001	637

prune156.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	6	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0.0b

Counts

92 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
9.5b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.5b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
30.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	290	994
1	1071	958
2	5001	942

prune220.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Merged error: 0.0b

Counts

82 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
10.1b	(cbrt (+ (* a a) (* b b)))
10.1b	(cbrt (+ (* a a) (* b b)))
10.1b	(cbrt (+ (* a a) (* b b)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

10.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
3.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
20.0ms	(cbrt (+ (* a a) (* b b)))
20.0ms	(cbrt (+ (* a a) (* b b)))
21.0ms	(cbrt (+ (* a a) (* b b)))

simplify121.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	264	1051
1	906	986
2	3837	912
3	5002	878

prune184.0ms

Filtered

75 candidates to 99 candidates (-32.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	99	6	105

Merged error: 0.0b

Counts

105 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
1.9b	(* (pow a 2) (pow b 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
16×	`unswap-sqr`
15×	`add-exp-log`
14×	`unpow-prod-down` `add-log-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l`
7×	`add-cube-cbrt`
6×	`pow-to-exp` `pow-exp`
5×	`add-cbrt-cube`
4×	`sum-log`
3×	`pow1` `diff-log`
2×	`distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

3 → 80

Calls

3 calls:

13.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
4.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* (pow a 2) (pow b 2))

series27.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
9.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
6.0ms	(* (pow a 2) (pow b 2))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	334	638
1	1402	555
2	5001	542

prune134.0ms

Filtered

50 candidates to 89 candidates (-78.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	89	6	95

Merged error: 0.0b

Counts

95 → 6

regimes211.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	32
1	29	32

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 69.726563%

Guaranteed chance to sample good point: 93.175403%

Results

528.0ms	8000×	body	80	valid
16.0ms	236×	body	80	invalid

Details

sample357.0ms

simplify95.0ms

prune3.0ms

localize16.0ms

rewrite27.0ms

series59.0ms

simplify70.0ms

prune156.0ms

localize20.0ms

rewrite23.0ms

series103.0ms

simplify41.0ms

prune220.0ms

localize22.0ms

rewrite25.0ms

series82.0ms

simplify121.0ms

prune184.0ms

localize13.0ms

rewrite27.0ms

series27.0ms

simplify48.0ms

prune134.0ms

regimes211.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling