Details

sample39.0ms

Algorithm

intervals

Results

24.0ms

656×

body

valid

simplify61.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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))
2.0ms	(+ (* a a) (* b b))
26.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* b b))
28.0ms	(+ (* a a) (* b b))
68.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (10.0ms)

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

prune173.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
15.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite160.0ms

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:

116.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
14.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series731.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
195.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
193.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
198.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify152.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	262	1815
1	942	1694
2	4261	1539
3	5001	1529

prune321.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.7b	(pow (sqrt (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))) 4)
15.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
9×	`cbrt-prod`
7×	`pow1`
6×	`add-exp-log` `pow-unpow` `sqrt-prod`
5×	`pow-pow`
4×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`pow-to-exp` `sqrt-pow1` `flip3-+` `pow-exp` `flip-+` `sqr-pow`
1×	`pow1/2` `sqrt-pow2`

Counts

4 → 70

Calls

4 calls:

4.0ms	(pow (+ (* a a) (* b b)) 2.0)
33.0ms	(pow (sqrt (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))) 4)
14.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series685.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (+ (* a a) (* b b)) 2.0)
196.0ms	(pow (sqrt (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))) 4)
187.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
195.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	352	980
1	1335	880
2	5001	824

prune531.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* (pow a 2) (pow b 2)))
0.9b	(* (pow a 2) (pow b 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
28×	`prod-exp`
23×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`unpow2` `sqr-pow`
9×	`associate-r` `add-cbrt-cube`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `add-log-exp`

Counts

2 → 76

Calls

2 calls:

10.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

series73.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* 2 (* (pow a 2) (pow b 2)))
37.0ms	(* (pow a 2) (pow b 2))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	229	393
1	907	329
2	5002	318

prune145.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

764.0ms

20310×

body

valid