Details

sample42.0ms

Algorithm

intervals

Results

27.0ms

643×

body

valid

simplify56.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite37.0ms

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:

6.0ms	(* 4.0 (* b b))
23.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
2.0ms	(+ (* a a) (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 4.0 (* b b))
63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
30.0ms	(+ (* a a) (* b b))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (10.0ms)

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

prune162.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.6b	(* (pow a 2) (pow b 2))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

142.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
6.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
13.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

series177.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
55.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms	(* 2 (* (pow a 2) (pow b 2)))
32.0ms	(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	382	781
1	1594	689
2	5001	676

prune240.0ms

Filtered

117 candidates to 61 candidates (52.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0) (* 4.0 (* b b)))
0.1b	(* (- (pow b 3)) b)
0.3b	(pow (/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
20.6b	(/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
28×	`associate-l`
24×	`unpow-prod-down` `times-frac`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`pow1` `difference-of-squares`
6×	`cube-prod` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`pow-unpow` `associate-r` `associate-/l*` `sqr-pow`
2×	`cube-mult` `flip3--` `flip3-+` `unpow3` `div-exp` `pow-exp` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-lft-neg-out` `pow-to-exp` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

141.0ms	(+ (pow (/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0) (* 4.0 (* b b)))
15.0ms	(* (- (pow b 3)) b)
20.0ms	(pow (/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
25.0ms	(/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ (pow (/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0) (* 4.0 (* b b)))
37.0ms	(* (- (pow b 3)) b)
140.0ms	(pow (/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b))) 2.0)
75.0ms	(/ (+ (* (- (pow b 3)) b) (pow a 4)) (- (* a a) (* b b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	601	1490
1	3161	1370
2	5002	1366

prune423.0ms

Filtered

135 candidates to 107 candidates (79.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (* b b) (+ (* 2 (pow a 2)) 4.0)) (pow b 4))
0.7b	(* (* b b) (+ (* 2 (pow a 2)) 4.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `associate-l` `sum-log` `*-commutative` `unswap-sqr`

Counts

2 → 36

Calls

2 calls:

13.0ms	(+ (* (* b b) (+ (* 2 (pow a 2)) 4.0)) (pow b 4))
21.0ms	(* (* b b) (+ (* 2 (pow a 2)) 4.0))

series131.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(+ (* (* b b) (+ (* 2 (pow a 2)) 4.0)) (pow b 4))
74.0ms	(* (* b b) (+ (* 2 (pow a 2)) 4.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	265	348
1	1536	304
2	5002	303

prune90.0ms

Filtered

42 candidates to 28 candidates (66.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes121.0ms

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

884.0ms

20640×

body

valid