Details

sample56.0ms

Algorithm

intervals

Results

31.0ms

668×

body

valid

simplify54.0ms

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

prune4.0ms

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	(+ (* a a) (* b b))
0.0b	(* 4.0 (* 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

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))
10.0ms	(* 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)

series214.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a a) (* b b))
29.0ms	(* 4.0 (* b b))
60.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
100.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (9.0ms)

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

prune225.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	2	71

Merged error: 0b

Counts

71 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.3b	(* (pow a 2) (pow b 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
28×	`prod-exp`
24×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`add-cbrt-cube` `unpow2` `sqr-pow`
9×	`associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-log-exp`
4×	`cbrt-unprod`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 87

Calls

3 calls:

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))

series125.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms	(* 2 (* (pow a 2) (pow b 2)))
34.0ms	(* (pow a 2) (pow b 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	297	518
1	1270	444
2	5001	432

prune418.0ms

Filtered

96 candidates to 47 candidates (49.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	96	2	98

Merged error: 0b

Counts

98 → 2

localize14.0ms

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)))
2.3b	(* (pow a 2) (pow b 2))

rewrite31.0ms

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))
8.0ms	(+ (+ (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:

34.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
23.0ms	(* 4.0 (* b b))
60.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
33.0ms	(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (48.0ms)

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

prune289.0ms

Filtered

120 candidates to 61 candidates (50.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	120	2	122

Merged error: 0b

Counts

122 → 2

regimes88.0ms

Accuracy

86.2% (0.1b remaining)

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

bsearch92.0ms

Steps

Iters	Range		Point
5	2.190530622938087e-76	7.24740059955196e-76	2.3023225040902804e-76
8	-0.005249672799317699	-2.515181766030432e-06	-0.00011045924450169089

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	19
1	39	19

end0.0ms

sample1.5s

Algorithm

intervals

Results

942.0ms

20238×

body

valid

Details

sample56.0ms

simplify54.0ms

prune4.0ms

localize10.0ms

rewrite26.0ms

series214.0ms

simplify38.0ms

prune225.0ms

localize13.0ms

rewrite22.0ms

series125.0ms

simplify46.0ms

prune418.0ms

localize14.0ms

rewrite31.0ms

series151.0ms

simplify57.0ms

prune289.0ms

regimes88.0ms

bsearch92.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling