Details

sample48.0ms

Algorithm

intervals

Results

27.0ms

713×

body

valid

simplify55.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

291.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
19.0ms	(* 4.0 (* b b))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series191.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
27.0ms	(* 4.0 (* b b))
97.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	264	417
1	954	380
2	3609	373
3	5001	373

prune137.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)
15.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite142.0ms

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:

10.0ms	(pow (+ (* a a) (* b b)) 2.0)
10.0ms	(pow (+ (* a a) (* b b)) 2.0)
59.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
61.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(pow (+ (* a a) (* b b)) 2.0)
97.0ms	(pow (+ (* a a) (* b b)) 2.0)
79.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify99.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (20.0ms)

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

prune276.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

15.4b	(sqrt (+ (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (* 4.0 (* b b))))
21.0b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.0b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.0b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

195.0ms	(sqrt (+ (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (* 4.0 (* b b))))
9.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series525.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (+ (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (* 4.0 (* b b))))
149.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
143.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
143.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	228	958
1	693	898
2	2745	897
3	5002	891

prune329.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
0.0b	(* 4.0 (pow b 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

64.0ms	(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
16.0ms	(* 4.0 (pow b 2))

series75.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
24.0ms	(* 4.0 (pow b 2))

simplify126.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	186	256
1	725	224
2	3434	220
3	5002	219

prune98.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes146.0ms

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	21	21
1	21	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

773.0ms

20279×

body

valid