Details

sample44.0ms

Algorithm

intervals

Results

28.0ms

672×

body

valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`fma-def` `add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

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

series237.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* a a) (* b b))
63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
32.0ms	(* 4.0 (* b b))
108.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5002	385

prune230.0ms

Filtered

86 candidates to 66 candidates (76.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (pow a 2))
1.5b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

6.0ms	(* 2 (pow a 2))
1.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series99.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* 2 (pow a 2))
75.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify136.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	139	196
1	607	173
2	3092	173
3	5001	167

prune134.0ms

Filtered

45 candidates to 30 candidates (66.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.0b	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
1.5b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down`
2×	`*-commutative` `fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

5.0ms	(* 2.0 (pow a 2))
4.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
1.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series194.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 2.0 (pow a 2))
68.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
24.0ms	(* 4.0 (* b b))
76.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	291	467
1	1199	418
2	5002	407

prune253.0ms

Filtered

89 candidates to 61 candidates (68.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.1b	(pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
29.8b	(cbrt (pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod` `add-log-exp`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp`
1×	`+-commutative` `fma-def` `flip3-+` `pow1/3` `sum-log` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

4.0ms	(+ (* a a) (* b b))
2.0ms	(pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
2.0ms	(cbrt (pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3))

series296.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a a) (* b b))
90.0ms	(pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3)
104.0ms	(pow (+ (* a a) (* b b)) 2.0)
69.0ms	(cbrt (pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	341	742
1	1493	680
2	5002	664

prune448.0ms

Filtered

93 candidates to 64 candidates (68.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample1.1s

Algorithm

intervals

Results

776.0ms

20591×

body

valid