Details

sample43.0ms

Algorithm

intervals

Results

23.0ms

666×

body

valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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))) 1.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`add-log-exp`
10×	`pow1` `add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `fma-neg` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`diff-log` `sum-log`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `fma-def` `flip3-+` `associate-r` `pow-exp` `associate--l+` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

18.0ms	(* 4.0 (* b b))
8.0ms	(+ (* a a) (* b b))
352.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series243.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 4.0 (* b b))
28.0ms	(+ (* a a) (* b b))
79.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
110.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	404	753
1	1693	603
2	5001	587

prune229.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)
16.6b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
16.6b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `pow-unpow` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

11.0ms	(pow (+ (* a a) (* b b)) 2.0)
10.0ms	(pow (+ (* a a) (* b b)) 2.0)
67.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
69.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (+ (* a a) (* b b)) 2.0)
110.0ms	(pow (+ (* a a) (* b b)) 2.0)
89.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
96.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify105.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	213	702
1	811	666
2	3265	656
3	5001	656

prune316.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (fma (* 4.0 b) b (pow a 4)) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `associate--l+` `add-cbrt-cube` `flip--` `fma-udef` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

7.0ms

(- (fma (* 4.0 b) b (pow a 4)) 1.0)

series84.0ms

Counts

1 → 3

Calls

1 calls:

83.0ms

(- (fma (* 4.0 b) b (pow a 4)) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	142	294
1	438	208
2	2731	197
3	5001	163

prune70.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

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	(- (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))) 1.0)
1.8b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`add-exp-log` `prod-diff`
8×	`associate-r`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `fma-neg` `associate-l` `prod-exp`
2×	`diff-log` `sum-log` `fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `flip3-+` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* 2.0 (pow a 2))
7.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
33.0ms	(- (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))) 1.0)
0.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series261.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 2.0 (pow a 2))
69.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
91.0ms	(- (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))) 1.0)
74.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	342	895
1	1460	746
2	5002	724

prune287.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes131.0ms

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	17	18
1	17	18

end0.0ms

sample1.2s

Algorithm

intervals

Results

750.0ms

20539×

body

valid