Details

sample42.0ms

Algorithm

intervals

Results

27.0ms

643×

body

valid

simplify59.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

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

series235.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
28.0ms	(+ (* a a) (* b b))
31.0ms	(* 4.0 (* b b))
106.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	322	413
1	1353	379
2	5001	379

prune174.0ms

Filtered

70 candidates to 49 candidates (70.0%)

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: 0.0b

Counts

71 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (pow a 2) (pow b 2)))
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))))
1.6b	(* (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:

7.0ms	(* 2 (* (pow a 2) (pow b 2)))
8.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
5.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* (pow a 2) (pow b 2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 2 (* (pow a 2) (pow b 2)))
56.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
51.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms	(* (pow a 2) (pow b 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	375	699
1	1611	622
2	5002	616

prune259.0ms

Filtered

113 candidates to 60 candidates (53.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	112	5	117

Merged error: 0b

Counts

117 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (pow b 2) (+ (* 2 (pow a 2)) 4.0)) (pow a 4)) 1.0)
0.0b	(* 2 (pow a 2))
0.0b	(+ (* (pow b 2) (+ (* 2 (pow a 2)) 4.0)) (pow a 4))
0.9b	(* (pow b 2) (+ (* 2 (pow a 2)) 4.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
14×	`add-exp-log`
12×	`*-un-lft-identity`
11×	`associate-r` `associate-l` `add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`prod-exp`
4×	`pow1` `unpow2` `sqr-pow`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-lft-in` `flip3-+` `diff-log` `associate-r/` `pow-exp` `sum-log` `-commutative` `cbrt-unprod` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

12.0ms	(- (+ (* (pow b 2) (+ (* 2 (pow a 2)) 4.0)) (pow a 4)) 1.0)
6.0ms	(* 2 (pow a 2))
15.0ms	(+ (* (pow b 2) (+ (* 2 (pow a 2)) 4.0)) (pow a 4))
9.0ms	(* (pow b 2) (+ (* 2 (pow a 2)) 4.0))

series271.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (+ (* (pow b 2) (+ (* 2 (pow a 2)) 4.0)) (pow a 4)) 1.0)
24.0ms	(* 2 (pow a 2))
81.0ms	(+ (* (pow b 2) (+ (* 2 (pow a 2)) 4.0)) (pow a 4))
79.0ms	(* (pow b 2) (+ (* 2 (pow a 2)) 4.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	425	707
1	2033	649
2	5002	649

prune260.0ms

Filtered

99 candidates to 67 candidates (67.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	100	4	104

Merged error: 0b

Counts

104 → 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	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
1.6b	(* (pow a 2) (pow b 2))

rewrite27.0ms

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:

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

series177.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
59.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
29.0ms	(* 4.0 (* b b))
31.0ms	(* (pow a 2) (pow b 2))

simplify62.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (53.0ms)

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

prune238.0ms

Filtered

106 candidates to 60 candidates (56.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

110 → 4

regimes142.0ms

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	15	8
1	15	8

end0.0ms

sample1.1s

Algorithm

intervals

Results

766.0ms

20683×

body

valid