Details

sample50.0ms

Algorithm

intervals

Results

34.0ms

676×

body

valid

simplify57.0ms

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 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)

rewrite21.0ms

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

series221.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a a) (* b b))
62.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
27.0ms	(* 4.0 (* b b))
102.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (10.0ms)

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

prune138.0ms

Filtered

70 candidates to 49 candidates (70.0%)

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: 0.0b

Counts

71 → 3

localize13.0ms

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)
15.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.7b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `pow-unpow` `sqrt-prod`
4×	`sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (+ (* a a) (* b b)) 2.0)
112.0ms	(pow (+ (* a a) (* b b)) 2.0)
94.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
93.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify105.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	202	652
1	753	636
2	3003	634
3	5002	634

prune198.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Merged error: 0.0b

Counts

79 → 3

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))))
3.1b	(* (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	(* 2 (* (pow a 2) (pow b 2)))
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	(* (pow a 2) (pow b 2))

series173.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 2 (* (pow a 2) (pow b 2)))
53.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
49.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
35.0ms	(* (pow a 2) (pow b 2))

simplify60.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (49.0ms)

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

prune201.0ms

Filtered

113 candidates to 60 candidates (53.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Merged error: 0b

Counts

116 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.2b	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
22.5b	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`sqr-pow`
6×	`pow-unpow`
5×	`pow-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`pow1/3` `associate-r` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

5.0ms	(* 4.0 (* b b))
6.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
9.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series396.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* b b))
125.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
104.0ms	(pow (+ (* a a) (* b b)) 2.0)
142.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	352	723
1	1324	703
2	5001	697

prune189.0ms

Filtered

110 candidates to 63 candidates (57.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Merged error: 0b

Counts

114 → 4

regimes109.0ms

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	17	18
1	17	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

946.0ms

20540×

body

valid