Details

sample49.0ms

Algorithm

intervals

Results

33.0ms

683×

body

valid

simplify58.0ms

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

localize10.0ms

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)

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:

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a a) (* b b))
63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
30.0ms	(* 4.0 (* b b))
105.0ms	(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

prune147.0ms

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: 0b

Counts

71 → 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)))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.5b	(* (pow a 2) (pow b 2))

rewrite30.0ms

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×	`*-un-lft-identity` `add-cbrt-cube` `unpow2` `sqr-pow`
9×	`associate-r`
8×	`add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`cbrt-unprod`
3×	`sum-log`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 90

Calls

3 calls:

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

series124.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
36.0ms	(* 2 (* (pow a 2) (pow b 2)))
33.0ms	(* (pow a 2) (pow b 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	330	587
1	1424	506
2	5001	495

prune168.0ms

Filtered

99 candidates to 50 candidates (50.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0b

Counts

103 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) (* 2 2.0))
33.5b	(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`pow1` `add-cbrt-cube`
9×	`times-frac`
6×	`unpow-prod-down`
4×	`pow-unpow` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `associate-r` `clear-num` `*-commutative` `flip--` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

6.0ms	(* 4.0 (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
15.0ms	(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* 4.0 (* b b))
107.0ms	(pow (+ (* a a) (* b b)) 2.0)
106.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
181.0ms	(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify65.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	429	1216
1	2085	1090
2	5001	1034

prune270.0ms

Filtered

94 candidates to 69 candidates (73.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	94	4	98

Merged error: 0b

Counts

98 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) (* 2 2.0))
2.0b	(* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0)))
3.2b	(+ (* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0))) (pow (+ (* a a) (* b b)) (* 2 2.0)))
43.6b	(/ (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)) (+ (* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0))) (pow (+ (* a a) (* b b)) (* 2 2.0))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
16×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac` `add-cbrt-cube`
14×	`pow1`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`associate-/l*`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `sum-cubes` `distribute-lft-out`
3×	`unpow-prod-down` `flip3-+` `associate-r` `associate-/r*` `flip-+`
2×	`associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-unpow` `flip3--` `pow-pow` `frac-2neg` `div-exp` `associate-l` `pow-exp` `clear-num` `sum-log` `*-commutative` `flip--` `div-inv` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
19.0ms	(* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0)))
21.0ms	(+ (* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0))) (pow (+ (* a a) (* b b)) (* 2 2.0)))
36.0ms	(/ (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)) (+ (* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0))) (pow (+ (* a a) (* b b)) (* 2 2.0))))

series940.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
112.0ms	(* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0)))
355.0ms	(+ (* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0))) (pow (+ (* a a) (* b b)) (* 2 2.0)))
365.0ms	(/ (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)) (+ (* (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0))) (pow (+ (* a a) (* b b)) (* 2 2.0))))

simplify107.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	559	2534
1	3009	2304
2	5001	2300

prune328.0ms

Filtered

108 candidates to 74 candidates (68.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	108	4	112

Merged error: 0b

Counts

112 → 4

regimes139.0ms

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

sample1.3s

Algorithm

intervals

Results

974.0ms

20368×

body

valid