Details

sample44.0ms

Algorithm

intervals

Results

28.0ms

664×

body

valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

9.0ms	(* 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)

series194.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 4.0 (* b b))
66.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify111.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	249	342
1	939	315
2	3536	315
3	5001	315

prune119.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 0b

Counts

57 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
12.3b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.3b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.3b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite35.0ms

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:

15.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
6.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series881.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
372.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
183.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
183.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify143.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	262	1815
1	942	1694
2	4261	1539
3	5001	1529

prune260.0ms

Filtered

99 candidates to 75 candidates (75.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	99	5	104

Merged error: 0b

Counts

104 → 5

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)))
2.9b	(* (pow a 2) (pow b 2))

rewrite29.0ms

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:

7.0ms	(+ (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))

series193.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
75.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
34.0ms	(* 2 (* (pow a 2) (pow b 2)))
34.0ms	(* (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	622
2	5001	616

prune198.0ms

Filtered

113 candidates to 60 candidates (53.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	113	5	118

Merged error: 0b

Counts

118 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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)))
2.9b	(* (pow a 2) (pow b 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `associate-l`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unpow2` `sqr-pow`
9×	`add-log-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
5.0ms	(* 4.0 (* b b))
7.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
7.0ms	(* (pow a 2) (pow b 2))

series151.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
23.0ms	(* 4.0 (* b b))
61.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
30.0ms	(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	400	683
1	1741	575
2	5002	568

prune178.0ms

Filtered

120 candidates to 61 candidates (50.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	120	5	125

Merged error: 0b

Counts

125 → 5

regimes110.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

763.0ms

20463×

body

valid