Details

sample54.0ms

Algorithm

intervals

Results

36.0ms

656×

body

valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
7×	`distribute-rgt-in` `fma-def` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

28.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms	(* (* a a) (+ 1.0 a))
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series313.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms	(* (* a a) (+ 1.0 a))
53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	564	828
1	2826	724
2	5001	715

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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)
13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`unpow-prod-down` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `rem-sqrt-square` `pow-unpow` `sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp`

Counts

4 → 80

Calls

4 calls:

4.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

series663.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(pow (+ (* a a) (* b b)) 2.0)
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
139.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	138	560
1	470	522
2	1671	512
3	5002	504

prune402.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

2.6b	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`add-sqr-sqrt`
17×	`sqrt-prod`
14×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
7×	`rem-sqrt-square`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/3`
2×	`pow1/2`

Counts

4 → 81

Calls

4 calls:

9.0ms	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
10.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series580.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
139.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
145.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	197	714
1	443	674
2	1374	670
3	5001	662

prune490.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (sqrt (pow (+ (* a a) (* b b)) 2.0)))
13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-prod`
17×	`cbrt-prod` `add-sqr-sqrt`
14×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
6×	`rem-sqrt-square` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 79

Calls

4 calls:

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

series594.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (sqrt (pow (+ (* a a) (* b b)) 2.0)))
148.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
141.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
152.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	192	711
1	421	664
2	1286	660
3	5001	655

prune486.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	21
1	27	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

20310×

body

valid