Details

analyze84.0ms

Algorithm

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

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4828	17
1	4828	17

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:

4.0ms	(+ (* a a) (* b b))
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)

series45.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify30.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5434	782

prune110.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
19.9b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.9b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.9b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

14.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series138.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
34.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
36.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
33.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5052	2354

prune284.0ms

Filtered

89 candidates to 121 candidates (-36.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	121	4	125

Merged error: 0b

Counts

125 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow b 4) (+ (pow a 4) (* a (* a (* b (* b 2))))))
0.0b	(+ (pow a 4) (* a (* a (* b (* b 2)))))
0.9b	(* a (* a (* b (* b 2))))
1.2b	(* a (* b (* b 2)))

rewrite33.0ms

Algorithm

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4966	1002
1	4966	1002

prune101.0ms

Filtered

45 candidates to 82 candidates (-82.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	82	4	86

Merged error: 0b

Counts

86 → 4

localize29.0ms

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)
3.6b	(+ (pow (+ (* a a) (* b b)) (* 2.0 2)) (* b (* b (* 4.0 (- (* b (* b 4.0)) (pow (+ (* a a) (* b b)) 2.0))))))
49.2b	(/ (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (* (pow 4.0 3) (pow b 6))) (+ (pow (+ (* a a) (* b b)) (* 2.0 2)) (* b (* b (* 4.0 (- (* b (* b 4.0)) (pow (+ (* a a) (* b b)) 2.0)))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `sub-neg` `associate-+r+`
6×	`pow1` `unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
10.0ms	(+ (pow (+ (* a a) (* b b)) (* 2.0 2)) (* b (* b (* 4.0 (- (* b (* b 4.0)) (pow (+ (* a a) (* b b)) 2.0))))))
23.0ms	(/ (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (* (pow 4.0 3) (pow b 6))) (+ (pow (+ (* a a) (* b b)) (* 2.0 2)) (* b (* b (* 4.0 (- (* b (* b 4.0)) (pow (+ (* a a) (* b b)) 2.0)))))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (+ (* a a) (* b b)) 2.0)
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
62.0ms	(+ (pow (+ (* a a) (* b b)) (* 2.0 2)) (* b (* b (* 4.0 (- (* b (* b 4.0)) (pow (+ (* a a) (* b b)) 2.0))))))
97.0ms	(/ (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (* (pow 4.0 3) (pow b 6))) (+ (pow (+ (* a a) (* b b)) (* 2.0 2)) (* b (* b (* 4.0 (- (* b (* b 4.0)) (pow (+ (* a a) (* b b)) 2.0)))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4976	3470
1	4976	3470

prune321.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	96	4	100

Merged error: 0b

Counts

100 → 4

regimes266.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	25	17
1	25	17

end0.0ms

sample503.0ms

Algorithm

intervals

Results

371.0ms	8000×	body	80	valid
0.0ms	7×	body	80	invalid

Details

analyze84.0ms

sample19.0ms

simplify64.0ms

prune9.0ms

localize10.0ms

rewrite22.0ms

series45.0ms

simplify30.0ms

prune110.0ms

localize15.0ms

rewrite32.0ms

series138.0ms

simplify62.0ms

prune284.0ms

localize13.0ms

rewrite33.0ms

series38.0ms

simplify50.0ms

prune101.0ms

localize29.0ms

rewrite45.0ms

series202.0ms

simplify72.0ms

prune321.0ms

regimes266.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample503.0ms

Profiling