Details

sample48.0ms

Algorithm

intervals

Results

31.0ms

678×

body

valid

simplify57.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`unpow-prod-down` `pow-unpow` `sum-log`
2×	`+-commutative` `flip3-+` `diff-log` `flip-+`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-exp` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

10.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
4.0ms	(+ (* a a) (* b b))
7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series279.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
27.0ms	(+ (* a a) (* b b))
70.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	330	556
1	1404	524
2	5001	517

prune165.0ms

Filtered

67 candidates to 51 candidates (76.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	4	68

Merged error: 0b

Counts

68 → 4

localize13.0ms

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 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))))
1.5b	(* (pow a 2) (pow b 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

8.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
11.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
5.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
8.0ms	(* (pow a 2) (pow b 2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
57.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
56.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
33.0ms	(* (pow a 2) (pow b 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	387	802
1	1681	732
2	5002	728

prune220.0ms

Filtered

106 candidates to 63 candidates (59.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Merged error: 0b

Counts

110 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
0.0b	(* 4.0 (* b b))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
1.5b	(* (pow a 2) (pow b 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

5.0ms	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
5.0ms	(* 4.0 (* b b))
8.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
8.0ms	(* (pow a 2) (pow b 2))

series179.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
24.0ms	(* 4.0 (* b b))
66.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
32.0ms	(* (pow a 2) (pow b 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	398	648
1	1813	559
2	5001	551

prune198.0ms

Filtered

106 candidates to 60 candidates (56.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Merged error: 0b

Counts

110 → 4

localize19.0ms

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)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
11.8b	(/ (- (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3) (pow 1.0 3)) (+ (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (* 1.0 1.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
75×	`times-frac`
64×	`difference-of-squares`
57×	`unpow-prod-down`
48×	`cube-prod`
40×	`add-cube-cbrt`
35×	`sqr-pow`
25×	`associate-/l*`
20×	`distribute-lft-out--`
9×	`add-exp-log` `pow-unpow`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`difference-cubes` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 171

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
41.0ms	(/ (- (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3) (pow 1.0 3)) (+ (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (* 1.0 1.0)))

series935.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (+ (* a a) (* b b)) 2.0)
105.0ms	(pow (+ (* a a) (* b b)) 2.0)
106.0ms	(pow (+ (* a a) (* b b)) 2.0)
621.0ms	(/ (- (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 3) (pow 1.0 3)) (+ (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (* 1.0 1.0)))

simplify111.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	562	6441
1	2242	6286
2	5001	6284

prune488.0ms

Filtered

183 candidates to 115 candidates (62.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	183	4	187

Merged error: 0b

Counts

187 → 4

regimes211.0ms

Accuracy

82.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 1.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

973.0ms

20550×

body

valid

Details

sample48.0ms

simplify57.0ms

prune2.0ms

localize13.0ms

rewrite26.0ms

series279.0ms

simplify42.0ms

prune165.0ms

localize13.0ms

rewrite34.0ms

series195.0ms

simplify59.0ms

prune220.0ms

localize14.0ms

rewrite28.0ms

series179.0ms

simplify61.0ms

prune198.0ms

localize19.0ms

rewrite64.0ms

series935.0ms

simplify111.0ms

prune488.0ms

regimes211.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling