Details

sample55.0ms

Algorithm

intervals

Results

34.0ms

623×

body

valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	15
1	161	15
2	459	15
3	1323	15
4	2992	15
5	5001	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

54.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
31.0ms	(* (* a a) (+ 1.0 a))
12.0ms	(pow (+ (* a a) (* b b)) 2.0)
27.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
48.0ms	(* (* a a) (+ 1.0 a))
107.0ms	(pow (+ (* a a) (* b b)) 2.0)
53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify72.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	504	702
1	2520	622
2	5002	622

prune244.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
8.5b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.5b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `associate-*r/` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `*-commutative` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

27.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
27.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
57.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
59.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
55.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
178.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
176.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	333	1082
1	1424	980
2	5002	978

prune307.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
9.1b	(cbrt (+ (* a a) (* b b)))
9.1b	(cbrt (+ (* a a) (* b b)))
9.1b	(cbrt (+ (* a a) (* b b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

41.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
5.0ms	(cbrt (+ (* a a) (* b b)))
8.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
98.0ms	(cbrt (+ (* a a) (* b b)))
95.0ms	(cbrt (+ (* a a) (* b b)))
97.0ms	(cbrt (+ (* a a) (* b b)))

simplify145.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	222	979
1	943	914
2	4107	856
3	5001	850

prune409.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
9.1b	(cbrt (+ (* a a) (* b b)))
9.1b	(cbrt (+ (* a a) (* b b)))
12.4b	(pow (+ (* a a) (* b b)) 1/3)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`cbrt-prod`
16×	`add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
12×	`pow1`
8×	`flip3-+` `pow1/3` `flip-+`
7×	`add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`unpow-prod-down` `pow-unpow`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `unpow1/3` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

42.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
5.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))
10.0ms	(pow (+ (* a a) (* b b)) 1/3)

series384.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
94.0ms	(cbrt (+ (* a a) (* b b)))
94.0ms	(cbrt (+ (* a a) (* b b)))
94.0ms	(pow (+ (* a a) (* b b)) 1/3)

simplify45.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	271	934
1	1333	744
2	5002	720

prune425.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	27
1	32	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20611×

body

valid