Details

analyze165.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 60.975638%

Guaranteed chance to sample good point: 96.28125%

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	8
1	41	8
2	67	8
3	119	8
4	309	8
5	1494	8
6	5001	8

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

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

6.0ms	(+ (* a a) (* b b))
5.0ms	(* 4.0 (* b b))
6.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a a) (* b b))
3.0ms	(* 4.0 (* b b))
15.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
22.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	366	432
1	1534	398
2	5001	390

prune108.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize12.0ms

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)
13.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
13.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite21.0ms

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:

4.0ms	(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 (* b b))))
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (+ (* a a) (* b b)) 2.0)
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
18.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
21.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify103.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	241	690
1	860	674
2	3574	656
3	5003	646

prune155.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Merged error: 0b

Counts

79 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.2b	(* (pow a 2) (pow b 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
28×	`prod-exp`
25×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`-un-lft-identity` `associate-l*` `add-cbrt-cube` `add-log-exp`
10×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `associate-r`
6×	`pow1`
4×	`sum-log` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

9.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
4.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

series36.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
9.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
8.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	375	699
1	1613	621
2	5001	616

prune157.0ms

Filtered

60 candidates to 113 candidates (-88.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	113	3	116

Merged error: 0b

Counts

116 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (neg (* 4.0 4.0)) (pow b 4))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) (* 2 2.0))
36.7b	(/ (+ (* (neg (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
10×	`unpow-prod-down`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`pow1` `associate-l`
4×	`pow-unpow` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `prod-exp` `associate-/r` `associate-/l` `unswap-sqr`
2×	`pow-pow` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `distribute-lft-neg-out` `distribute-lft-neg-in` `neg-mul-1` `flip3--` `distribute-rgt-neg-in` `frac-2neg` `flip3-+` `div-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (neg (* 4.0 4.0)) (pow b 4))
7.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
15.0ms	(/ (+ (* (neg (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (neg (* 4.0 4.0)) (pow b 4))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)
22.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
40.0ms	(/ (+ (* (neg (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify80.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	534	1353
1	2700	1227
2	5003	1222

prune229.0ms

Filtered

79 candidates to 104 candidates (-31.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	3	107

Merged error: 0b

Counts

107 → 3

regimes191.0ms

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	17	18
1	17	18

end0.0ms

analyze141.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 60.975638%

Guaranteed chance to sample good point: 96.28125%

sample480.0ms

Algorithm

intervals

Results

351.0ms	8000×	body	80	valid
0.0ms	3×	body	80	invalid

Details

analyze165.0ms

sample19.0ms

simplify56.0ms

prune3.0ms

localize9.0ms

rewrite23.0ms

series45.0ms

simplify45.0ms

prune108.0ms

localize12.0ms

rewrite21.0ms

series83.0ms

simplify103.0ms

prune155.0ms

localize12.0ms

rewrite30.0ms

series36.0ms

simplify58.0ms

prune157.0ms

localize19.0ms

rewrite34.0ms

series89.0ms

simplify80.0ms

prune229.0ms

regimes191.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze141.0ms

sample480.0ms

Profiling