Details

sample55.0ms

Algorithm

intervals

Results

37.0ms

676×

body

valid

simplify52.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`pow-to-exp` `flip3--` `pow-pow` `associate-l` `pow-exp` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
50.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
107.0ms	(pow (+ (* a a) (* b b)) 2.0)
48.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	391	706
1	1680	606
2	5001	592

prune267.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
0.6b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
19×	`add-cbrt-cube`
18×	`add-sqr-sqrt` `prod-diff`
15×	`distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in`
9×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`sub-neg` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

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

series256.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (+ (* a a) (* b b)) 2.0)
47.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
52.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	304	905
1	1350	773
2	5002	753

prune487.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (- 1.0 (* 3.0 a)))
10.8b	(cbrt (+ (* a a) (* b b)))
10.8b	(cbrt (+ (* a a) (* b b)))
10.8b	(cbrt (+ (* a a) (* b b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
6×	`cbrt-div` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

23.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
93.0ms	(cbrt (+ (* a a) (* b b)))
93.0ms	(cbrt (+ (* a a) (* b b)))
115.0ms	(cbrt (+ (* a a) (* b b)))

simplify47.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	331	646
1	1480	584
2	5001	567

prune399.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (+ (* a a) (* b b)))
10.1b	(sqrt (+ (* a a) (* b b)))
10.8b	(cbrt (+ (* a a) (* b b)))
10.8b	(cbrt (+ (* a a) (* b b)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `hypot-def`

Counts

4 → 66

Calls

4 calls:

3.0ms	(sqrt (+ (* a a) (* b b)))
3.0ms	(sqrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* a a) (* b b)))
41.0ms	(sqrt (+ (* a a) (* b b)))
94.0ms	(cbrt (+ (* a a) (* b b)))
93.0ms	(cbrt (+ (* a a) (* b b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	153	468
1	493	440
2	1626	434
3	5002	432

prune478.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.0b

regimes114.0ms

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	13
1	21	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20274×

body

valid