Details

analyze85.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample20.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

valid

simplify66.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4828	17
1	4828	17

prune7.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize10.0ms (0.4%)

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 (1%)

Algorithm

1×	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:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(+ (* a a) (* b b))

series47.0ms (2%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (+ (* a a) (* b b)) 2.0)
16.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(+ (* a a) (* b b))
3.0ms	(* 4.0 (* b b))

simplify33.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5434	782

prune142.0ms (6%)

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

localize15.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (* a (* a (* b (* b 2)))))
0.0b	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
0.3b	(* a (* a (* b (* b 2))))
0.5b	(* a (* b (* b 2)))

rewrite32.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
8×	`*-un-lft-identity`
6×	`add-sqr-sqrt` `add-cube-cbrt` `associate-l`
4×	`sum-log`
2×	`+-commutative` `flip3-+` `associate-r` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

9.0ms	(* a (* a (* b (* b 2))))
9.0ms	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
7.0ms	(* a (* b (* b 2)))
5.0ms	(+ (pow a 4) (* a (* a (* b (* b 2)))))

series35.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
9.0ms	(+ (pow a 4) (* a (* a (* b (* b 2)))))
7.0ms	(* a (* a (* b (* b 2))))
7.0ms	(* a (* b (* b 2)))

simplify51.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4966	1002
1	4966	1002

prune175.0ms (7.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	82	3	85

Merged error: 0b

Counts

85 → 3

localize17.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow b 2.0))
0.0b	(+ (+ (pow b (* 2.0 2)) (* a (* a (* 2.0 (pow b 2.0))))) (* 4.0 (* b b)))
0.3b	(* a (* a (* 2.0 (pow b 2.0))))
0.5b	(* a (* 2.0 (pow b 2.0)))

rewrite30.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

9.0ms	(+ (+ (pow b (* 2.0 2)) (* a (* a (* 2.0 (pow b 2.0))))) (* 4.0 (* b b)))
8.0ms	(* a (* a (* 2.0 (pow b 2.0))))
6.0ms	(* a (* 2.0 (pow b 2.0)))
5.0ms	(* 2.0 (pow b 2.0))

series146.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(* 2.0 (pow b 2.0))
38.0ms	(* a (* a (* 2.0 (pow b 2.0))))
32.0ms	(* a (* 2.0 (pow b 2.0)))
17.0ms	(+ (+ (pow b (* 2.0 2)) (* a (* a (* 2.0 (pow b 2.0))))) (* 4.0 (* b b)))

simplify68.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4961	1049
1	4961	1049

prune214.0ms (9.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	91	3	94

Merged error: 0b

Counts

94 → 3

localize23.0ms (1%)

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (pow b 4))
0.3b	(pow (+ (* a a) (* b b)) (* 2.0 2))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
36.8b	(/ (- (pow (+ (* a a) (* b b)) (* 2.0 2)) (* 4.0 (* 4.0 (pow b 4)))) (- (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))))

rewrite32.0ms (1.4%)

Algorithm

1×	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`
4×	`pow-unpow` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `associate-l` `pow-exp` `prod-exp` `associate-/r` `associate-/l` `unswap-sqr`
2×	`flip3--` `pow-pow` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 89

Calls

4 calls:

15.0ms	(/ (- (pow (+ (* a a) (* b b)) (* 2.0 2)) (* 4.0 (* 4.0 (pow b 4)))) (- (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))))
5.0ms	(* 4.0 (pow b 4))
5.0ms	(pow (+ (* a a) (* b b)) (* 2.0 2))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series98.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (- (pow (+ (* a a) (* b b)) (* 2.0 2)) (* 4.0 (* 4.0 (pow b 4)))) (- (pow (+ (* a a) (* b b)) 2.0) (* b (* b 4.0))))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
22.0ms	(pow (+ (* a a) (* b b)) (* 2.0 2))
4.0ms	(* 4.0 (pow b 4))

simplify66.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4928	2231
1	4928	2231

prune292.0ms (12.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	101	3	104

Merged error: 0b

Counts

104 → 3

regimes124.0ms (5.3%)

Accuracy

Total 0.9b remaining (99.3%)

Threshold costs 0.9b (99.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms (0%)

sample508.0ms (21.5%)

Algorithm

1×

intervals

Results

368.0ms	8000×	body	80	valid
0.0ms	6×	body	80	invalid

Details

analyze85.0ms (3.6%)

sample20.0ms (0.8%)

simplify66.0ms (2.8%)

prune7.0ms (0.3%)

localize10.0ms (0.4%)

rewrite23.0ms (1%)

series47.0ms (2%)

simplify33.0ms (1.4%)

prune142.0ms (6%)

localize15.0ms (0.7%)

rewrite32.0ms (1.4%)

series35.0ms (1.5%)

simplify51.0ms (2.2%)

prune175.0ms (7.4%)

localize17.0ms (0.7%)

rewrite30.0ms (1.3%)

series146.0ms (6.2%)

simplify68.0ms (2.9%)

prune214.0ms (9.1%)

localize23.0ms (1%)

rewrite32.0ms (1.4%)

series98.0ms (4.1%)

simplify66.0ms (2.8%)

prune292.0ms (12.4%)

regimes124.0ms (5.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample508.0ms (21.5%)

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