Details

sample41.0ms

Algorithm

intervals

Results

27.0ms

620×

body

valid

simplify58.0ms

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

localize9.0ms

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	(+ (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)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

11.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
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)

series256.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
23.0ms	(* 4.0 (* b b))
98.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify142.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	309	549
1	1144	520
2	4418	513
3	5002	513

prune154.0ms

Filtered

75 candidates to 53 candidates (70.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 0.0b

Counts

76 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
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)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`unpow-prod-down` `pow-unpow`
7×	`pow1` `add-exp-log`
5×	`cbrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
2×	`cbrt-div`
1×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

11.0ms	(cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
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)

series486.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
102.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify99.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	216	633
1	740	599
2	2851	597
3	5001	595

prune238.0ms

Filtered

78 candidates to 60 candidates (76.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Merged error: 0b

Counts

82 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.4b	(* (pow a 2) (pow b 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

11.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
8.0ms	(* (pow a 2) (pow b 2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
41.0ms	(* 2 (* (pow a 2) (pow b 2)))
32.0ms	(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	327	656
1	1353	573
2	5002	554

prune172.0ms

Filtered

103 candidates to 51 candidates (49.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	103	4	107

Merged error: 0b

Counts

107 → 4

localize23.0ms

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)
10.1b	(cbrt (- (* (+ (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)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow`
7×	`pow1` `add-exp-log`
4×	`cbrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
2×	`cbrt-div`
1×	`flip3--` `pow1/3` `flip--` `difference-of-squares`

Counts

4 → 65

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)
18.0ms	(cbrt (- (* (+ (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)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (+ (* a a) (* b b)) 2.0)
104.0ms	(pow (+ (* a a) (* b b)) 2.0)
102.0ms	(pow (+ (* a a) (* b b)) 2.0)
208.0ms	(cbrt (- (* (+ (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)))

simplify120.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	206	816
1	756	764
2	3479	762
3	5002	761

prune281.0ms

Filtered

77 candidates to 60 candidates (77.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	77	4	81

Merged error: 0b

Counts

81 → 4

regimes165.0ms

Accuracy

90% (0.1b remaining)

Error of 0.1b 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

sample1.2s

Algorithm

intervals

Results

891.0ms

20276×

body

valid

Details

sample41.0ms

simplify58.0ms

prune2.0ms

localize9.0ms

rewrite29.0ms

series256.0ms

simplify142.0ms

prune154.0ms

localize14.0ms

rewrite26.0ms

series486.0ms

simplify99.0ms

prune238.0ms

localize13.0ms

rewrite30.0ms

series126.0ms

simplify56.0ms

prune172.0ms

localize23.0ms

rewrite34.0ms

series519.0ms

simplify120.0ms

prune281.0ms

regimes165.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling